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The Pennsylvania State University
The Graduate School
LOUDSPEAKER ARRAY AND TESTING FACILITIES FOR
PERFORMING LARGE VOLUME ACTIVE NOISE CANCELLING
MEASUREMENTS
A Thesis In Acoustics
by Keagan Downey
© 2020 Keagan Downey
Submitted in Partial Fulfillment of the Requirements
for the Degree of Master of Science
December 2020
ii
The thesis of Keagan Downey was reviewed and approved by the following:
Stephen C. Thompson
Research Professor of Acoustics
Thesis Advisor
Michelle C. Vigeant
Associate Professor of Acoustics and Architectural Engineering
Daniel A. Russell
Teaching Professor of Acoustics and Distance Education Coordinator
Victor W. Sparrow Director, Graduate Program in Acoustics
United Technologies Corporation Professor of Acoustics
iii
Abstract Modern advents in audio technology have facilitated the research and development of
active noise cancelling (ANC) systems for large volume applications. The principal
objectives of this research have been to mitigate sound passing through open windows
using a multi-channel ANC system while also retaining sufficient air and daylight
ventilation. Many research groups have shown promising numerical results, but no
group has experimentally validated a design which effectively optimizes both design
considerations. Previously, the Penn State University Transducer Development
Laboratory (TDL) developed a unique ANC system design which utilized a beam
forming optimization algorithm to determine the digital filters needed for the system’s
secondary source array. The array design was termed a sparse array and was a unique
design which sought to optimize ANC performance and ventilation. The numerical
models for this ANC system predicted similar noise reduction results in comparison to
other leading researchers while still providing significant ventilation. As with many
other researchers though, experimentally validating these numerical results has proved
challenging. The research covered in this thesis has focused primarily on the iterative
development of the secondary source array to be used in the proposed ANC system.
This development included significant improvements to the array’s driver frequency
responses and the array frame’s structural design. The improvements made during the
third iteration development yielded an array substantially more capable of obtaining
quality ANC measurements than all previous designs. Additionally, a new
measurement facility was constructed in which ANC reductions of at least 15 dB were
determined to be accurately measurable from 300-1500 Hz. This facility was a
significant improvement from the previously used facility and would increase
measurement efficiency considerably. Between the improvements made to the array
design and measurement facility, the ability to obtain accurate experimental results
which validate the proposed design’s theoretical results was improved significantly.
iv
Table of Contents List of Figures vii
List of Tables xv
Acknowledgements xvi
Chapter 1: Introductory Material 1
1.1 Project Overview ........................................................................................ 1
1.2 History of Active Noise Cancelling ............................................................. 2
1.3 ANC System Overview ............................................................................... 3
1.2.1 ANC Fundamentals .................................................................................. 3
1.2.2 Large Volume ANC.................................................................................. 4
1.2.3 ANC Performance vs. Ventilation ............................................................. 7
1.3 PSU Research ............................................................................................. 8
1.3.1 Sparse Arrays and Beam Forming ............................................................. 8
1.3.2 Optimization Overview............................................................................. 11
1.3.3 Simulated Results ..................................................................................... 13
Chapter 2: Experimental Design Overview 16
2.1 Generic Experimental Method ..................................................................... 16
2.2 External Experimental Methods .................................................................. 17
2.3 Internal Experimental Methods ................................................................... 19
2.3.1 Methodology ............................................................................................ 19
2.3.2 Measurement Facility ............................................................................... 21
2.3.3 Array Iteration 1: Design .......................................................................... 23
2.3.4 Array Iteration 1: Experimental Testing .................................................... 25
Chapter 3: Array Iteration 2 28
3.1 Design......................................................................................................... 28
3.1.1 Transducers .............................................................................................. 28
3.1.2 Mechanical Design ................................................................................... 30
3.2 Measurements ............................................................................................. 33
3.2.1 Frequency Response Measurement Method .............................................. 34
v
3.2.2 Frequency Response Measurement Results ............................................... 38
3.2.3 Noise Cancelling Measurement Results .................................................... 44
3.2.4 Result Summary ....................................................................................... 46
Chapter 4: Array Iteration 3 47
4.1 Mechanical Design .................................................................................... 47
4.1.1 Array Frame ............................................................................................ 47
4.1.2 Closed-Box Baffles................................................................................. 49
4.2 Acoustic Design .......................................................................................... 52
4.2.1 Closed-Box Baffle Modeling.................................................................. 52
4.2.2 Frequency Response Measurement Results ........................................... 55
4.2.3 Equalization Filters ................................................................................. 64
Chapter 5: Measurement Facility 72
5.1 Selection and Construction .......................................................................... 72
5.2 Transmission Loss Overview ...................................................................... 73
5.3 Transmission Loss Measurement Method .................................................... 75
5.4 Decibel Arithmetic ...................................................................................... 82
5.5 Transmission Loss Measurement Results .................................................... 84
Chapter 6: Concluding Material 89
6.1 Research Summary ..................................................................................... 89
6.1.1 Project Foundation.................................................................................... 89
6.1.2 Array Iteration 2 ....................................................................................... 89
6.1.3 Iteration 3 ................................................................................................. 90
6.1.4 Lab Facility Development ......................................................................... 90
6.2 Future Work ................................................................................................ 91
6.2.1 MATLAB................................................................................................. 91
6.2.2. Array Design Improvements .................................................................... 91
6.2.4. Further Measurement Facility Improvements ........................................... 93
6.3 Final Conclusions ........................................................................................ 94
6.3.1 Results ..................................................................................................... 94
6.3.2 Future Applications .................................................................................. 94
Appendix A: Speaker Specifications 96
Appendix B: Measurement Facility 98
vi
Appendix C: Self Noise Correction 109
Appendix D: Coding Improvements 110
Bibliography 129
vii
List of Figures Figure 1: This diagram shows an ideal noise cancellation scenario for a pure tone signal.
[18] .......................................................................................................................... 3
Figure 2: The noise signal would be continuously recorded by the feedforward and
feedback microphones. The signals would then be filtered using a digital signal
processing chip. After processing, the anti-noise signal is played through the same
speaker used for general audio listening. The result is localized noise reduction inside
the ear canal. ............................................................................................................ 4
Figure 3: The noise signals are captured using the two types of microphones, filtered
and phase inverted using the control systems, and introduced into the room at the noise
source (window) to globally reduce the noise levels inside the room. ....................... 6
Figure 4: The left array shows the speaker layout for an edge-distributed array while
the right shows that for a distributed array. ............................................................... 8
Figure 5: The four-cell sparse array consists of a grid of four squares with speakers
distributed along the grid lines. This layout combines edge-distributed and distributed
in a more optimal geometry. ..................................................................................... 9
Figure 6: The balloon-like figure is a MATLAB generated theoretical beam pattern
which represents the sound field generated when plane waves impinge on a rectangular
opening. [18] .......................................................................................................... 10
Figure 7: From left to right, the figure shows a uniform velocity profile, k-space Fourier
transform, and directivity pattern of a plane wave interacting with a large rectangular
opening. [22] .......................................................................................................... 12
Figure 8: The theoretical beam patterns for the noise and anti-noise pressure fields are
compared. Miller’s theoretical simulations showed near perfect cancellation results
were possible using a sparse array up to 1200 Hz. [18] ........................................... 15
viii
Figure 9: Generic experimental ANC design with elements similar to those shown in
Figs. 2 and 3. [18] .................................................................................................. 16
Figure 10: The reduced experimental design was developed specifically to analyze the
effectiveness of the beam filtered secondary source array. The control system would
prescribe audio signals to the primary and secondary sources while a separate control
system recorded the resultant audio data. ................................................................ 20
Figure 11: The diagram above comes from a research thesis by Paul Bauch [1] and
gives a dimensioned, 3-D perspective of the measurement facility used. The circle
shows the window used for transmission between the rooms. Note that this figure
shows the chamber prior to a 2012 remodel which saw some minor geometry changes.
.............................................................................................................................. 21
Figure 12: The figure shows an example of how reflections can cause challenges when
performing acoustic measurements. While the reverberation time was never officially
measured, it was generally estimated to be 4-6 seconds. ......................................... 22
Figure 13: The line array above was one of 12 units installed in the first iteration of the
array design. [18] ................................................................................................... 24
Figure 14: The image shows the first array iteration installed in the transmission
window of the coupled chambers. In this measurement setup, the anechoic chamber
visible through the window is the source room, while the reverberant chamber is the
receiving room. [18] ............................................................................................... 24
Figure 15: Theoretical and experimental directivity patterns are compared at specific
frequencies. In some instances, such as the 400 and 1100 Hz plots, the array beam
pattern matched the theoretical pattern fairly well. However, other examples, such as
the 700 and 1000 Hz plots, show poor matching. [18] ............................................ 26
Figure 16: The driver to the left is the 3.5-inch Dayton ND91-8 which was used on the
exterior of the array. The driver to the right is a 1.75-inch Tang Band W2121s which
was used on the interior of the array. ...................................................................... 29
ix
Figure 17: The specified frequency response of the Dayton ND91-8 driver is shown
above and is fairly flat in the frequency range of operation. .................................... 29
Figure 18: The Tang Band W2121s frequency response, shown above in red, has more
variability than the Dayton driver’s frequency response.......................................... 30
Figure 19: The drawing above was used to program the CNC router used for the array
machining. Using the router allowed for much finer detail in the cuts and more
consistency for future array iterations. The dimensions are given in inches............. 31
Figure 20: All speaker holes were cut by the CNC router to be the exact sizes necessary
to fit the selected drivers. The blue circle highlights the finely cut interior driver
mounting holes. ...................................................................................................... 32
Figure 21: The exterior drivers were fastened to the array using four screws displayed
in the figure using red circles. The interior drivers were press fit into the holes and
glued in place. The glue was placed along the circumference of the drivers as shown
with the blue circle. ................................................................................................ 33
Figure 22: The figure provides a visual representation of the input-output system used
to define the transfer function of the measured speaker........................................... 34
Figure 23: The mapping shows the signal flow in both the time and frequency domain.
At any point in the signal chain, translation to and from either domain is possible. . 35
Figure 24: The diagram shows the signal chain used throughout this research for
performing frequency response measurements. The left side of the diagram shows the
output signal chain while the right side shows the input signal chain. ..................... 37
Figure 25: In the image, the array is shown mounted on a wooden stand. The
measurement microphone is shown towards the top of the image. An extension was
added to the microphone stand to ensure the microphone was out of the near-field sound
radiation from the speakers. (Miller 2018) .............................................................. 38
Figure 26: Frequency responses (magnitude) for the Dayton, or exterior, drivers. The
frequency range of most importance is between the vertical red lines. .................... 39
x
Figure 27: Frequency responses (magnitude) for the Tang Band, or exterior, drivers.
The frequency range of most importance is between the vertical red lines. ............. 39
Figure 28: Frequency responses (phase) for the Dayton drivers. Responses were
expected to be linear and tightly grouped. .............................................................. 40
Figure 29: Frequency responses (phase) for the Tang Band drivers. Responses were
again expected to be linear and tightly grouped. ..................................................... 40
Figure 30: Both plots show different magnitude response groupings for symmetric
interior driver locations. Both sets of responses share many similarities, particularly
above 700 Hz. ........................................................................................................ 41
Figure 31: Both plots show different magnitude response groupings for symmetric
exterior driver locations. Both sets of responses share many similarities throughout the
entire frequency range. ........................................................................................... 42
Figure 32: The diagram shows the possible ways back-radiated sound could reach the
front of the array. If back-radiated sound reaches the measurement microphones, the
frequency response data would likely be corrupted. ................................................ 43
Figure 33: In the image, the array is set up facing into the reverberant chamber which
again served as the receiving room. A measurement microphone is shown a short
distance in front of the array. The anechoic chamber, which again served as the source
room, is shown through the window with a primary source set up for the measurements.
(Miller 2018) .......................................................................................................... 44
Figure 34: The third array frame designed is shown fully dimensioned using AutoCAD.
The dimensions are again in inches. ....................................................................... 48
Figure 35: The arrays are placed in chronological order from left to right. The leftmost
frame is iteration 1 (plywood), the center frame is iteration 2 (MDF), and the rightmost
frame is iteration 3 (MDF). .................................................................................... 48
Figure 36: The left image shows an interior driver enclosure with the leads exiting
through the PVC. The right image shows an exterior driver. The leads for these
eventually ran underneath the enclosures. ............................................................... 50
xi
Figure 37: Output signal chain and wiring to the speakers. ..................................... 51
Figure 38: The left image shows the painted back side of the array. The right image
shows the front side of the painted array. One visible downside of the wiring method
used is its disarray. ................................................................................................. 51
Figure 39: The LTspice circuit model approximates a speaker in a closed-box baffle.
Section A of the circuit represents the electrical domain, section B of the circuit
represents the mechanical domain, and section C of the circuit represents the acoustical
domain. .................................................................................................................. 52
Figure 40: The figure shows the Dayton driver’s theoretical magnitude response. The
input amplitude was set such that the maximum magnitude value was close to 0 dB.
The frequency range was limited to 80-10,000 Hz. ................................................. 54
Figure 41: The figure shows Tang Band driver’s theoretical magnitude response. .. 54
Figure 42: Frequency responses (magnitude) for the Dayton drivers. The responses
showed significant improvement with a tight grouping and less than 5 dB of variation
from each other. ..................................................................................................... 56
Figure 43: Frequency responses (magnitude) for the Tang Band drivers. The responses
showed no improvement with poor grouping and large variations........................... 56
Figure 44: Frequency responses (phase) for the Dayton drivers. The responses are
tightly grouped. ...................................................................................................... 57
Figure 45: Frequency responses (phase) for the Tang Band drivers. The responses are
not tightly grouped. ................................................................................................ 57
Figure 46: Frequency response comparison (magnitude) for the Dayton drivers with
and without closed-box baffles, or back volumes. ................................................... 58
Figure 47: Frequency response comparison (magnitude) for the Tang Band drivers with
and without closed-box baffles, or back volumes. ................................................... 58
Figure 48: The image on the left shows the entire array where the interior drivers have
putty seals added. The right image shows a close-up of one driver with the putty added.
xii
While the putty would not be viable as a long-term solution, the addition provided a
quality temporary resolution. .................................................................................. 60
Figure 49: New frequency responses (magnitude) for the Tang Band drivers. The new
magnitude responses are significantly better than previously measured. While they are
not as smooth and tightly grouped as the Dayton responses shown in Fig. 42, the Tang
Band responses are much improved. ....................................................................... 60
Figure 50: Frequency responses (phase) for the Tang Band drivers. The responses are
grouped significantly tighter than previously shown in Fig. 45. .............................. 61
Figure 51: Frequency response comparison (magnitude) for the Tang Band drivers with
and without putty and closed-box baffles. The magnitude responses were improved
significantly. .......................................................................................................... 61
Figure 52: Averaged magnitude response for the Dayton drivers compared to LTspice
simulated magnitude response. The ideal and measured responses match quite well.62
Figure 53: Averaged magnitude response for the Tang Band drivers compared to
LTspice simulated magnitude response. The ideal and measured responses match
relatively well. ....................................................................................................... 63
Figure 54: The plot to the left shows an arbitrary driver’s magnitude response measured
using the methods discussed previously. The second plot shows that same response
along with the inversion of itself. ........................................................................... 64
Figure 55:. The left plot shows the bandpass filter magnitude response used to tame the
extreme gains of the inverted filter at low and high frequencies. The right plot shows
the bandpass filter combined with the inverted transfer function to form the total EQ
filter for that specific driver. ................................................................................... 65
Figure 56: The left plot shows the total EQ filter and original magnitude response of
the driver. Multiplying those two responses together yields the ideal, equalized
response shown in the right plot. ............................................................................ 65
xiii
Figure 57: The plot compares the original input signal to the filtered input signal. The
filtered sweep has an amplitude change somewhat similar to the filter magnitude
response. ................................................................................................................ 66
Figure 58: Equalized magnitude responses for the Dayton drivers. The green dashed
lines show that the responses vary by less than 5 dB. Note that the responses are now
normalized by 1 as opposed to the max value as done previously. This helps to better
visualize the quality of the EQ filters. ..................................................................... 67
Figure 59: Equalized magnitude responses for the Tang Band drivers. The green dashed
lines show that the responses nearly vary by less than 5 dB. ................................... 68
Figure 60: The plot shows an equalized magnitude response when the measurement
environment is untouched between the initial frequency response and the EQ’d
frequency response measurements. The equalized response matches the ideal EQ’d
response very well. ................................................................................................. 69
Figure 61: The plot shows the same filter frequency response shown in figure 55 with
smoothing and no smoothing. The smoothing was generated using a 30-point moving
average filter. ......................................................................................................... 71
Figure 62: Fully constructed sound isolation chamber. The open door shows the foam
paneling used to cover the interior of the room. The stock window for the Whisper
Room products was conveniently similar in size to the array. The total construction
time was around two months. ................................................................................. 73
Figure 63: The figure above supports the below example. In the figure, the noise source
is located to the left. A wall with a secondary source array is shown in the center with
a measurement microphone shown to the right. The arrows represent the noise
propagation paths. .................................................................................................. 74
Figure 64: The figure shows the estimated amount of sound isolation at octave bands.
The sound isolation in the frequency region of interest appears to be steadily around 25
dB. ......................................................................................................................... 75
xiv
Figure 65: The image on the left shows the sound level meter mounted on a stand as
used for measuring the noise floor in Room 22. The image on the right shows the front
panel of the sound level meter. ............................................................................... 76
Figure 66: Z-weighted Room 22 noise floor at 1/3-octave bands. The total, A-weighted
sound pressure level is given in the top-right corner of the figure. .......................... 77
Figure 67: Z-weighted Whisper Room noise floor at 1/3-octave bands. The total, A-
weighted sound pressure level is given in the top-right corner of the figure. Note the
increased infrasonic octave bands on the left end of the figure. ............................... 77
Figure 68: The amplifier used was a Crown XLS 2500 and was provided by the SPRAL
lab. ......................................................................................................................... 79
Figure 69: The left image is of the omnidirectional subwoofer, and the right image is
of the omnidirectional mid-range speaker. Fundamental acoustics serves to remind that
lower frequency sources radiate with a more omnidirectional directivity. Hence,
subwoofer requires only two unique drivers while the mid-range source contains twelve
to achieve omnidirectional radiation. These sources were generously provided by the
SPRAL acoustics lab [6]. ....................................................................................... 80
Figure 70: The figure represents a top-down view of the lab space and experimental
setup for the transmission loss measurements. Note that the secondary measurement
locations were oriented at differing heights. The figure also shows the output signal
chain running from the controller, through the amp, and to the speakers. ................ 81
Figure 71: Z-weighted Room 22 measured white noise levels at 1/3-octave bands. . 84
Figure 72: Z-weighted Whisper Room measured white noise levels at 1/3-octave bands.
.............................................................................................................................. 85
Figure 73: Z-weighted transmission loss measured with white noise levels at 1/3-octave
bands. The transmission loss values are expressed as negative, implying sound reduced.
The figure shows an increasing amount of reduction with frequency, which was
expected. ................................................................................................................ 86
xv
List of Tables
Table 1: The chart covers a range of experimental results from various ANC
measurement methods. Note that some results seem to share similarities with Miller’s
simulations, where reduction upwards of 15 dB had been measured between 500-2000
Hz. Note that the references in the table do NOT correspond to references in this
paper.[16]............................................................................................................... 18
Table 2: The Tang Band and Dayton driver Thiele Small parameters used in the
theoretical models are compared. ........................................................................... 53
Table 3: Sound pressure levels in dB which reveal why the Whisper Room was chosen
to be the receiving room. ........................................................................................ 79
Table 4: Measured sound isolation compared to projected (from Fig. 64) sound
isolation at relevant octave bands. .......................................................................... 87
Table 5: Measurable noise cancellation possible using an ANC system in the Whisper
Room over the primary frequency range of operation. ............................................ 88
xvi
Acknowledgements I would like to first thank my advisor, Dr. Stephen Thompson, for giving me the
opportunity to work with him on this amazing project. While expectations shifted
significantly from the start to end of this project, Dr. Thompson always worked hard to
provide the best opportunities for my success. For that, I will always be grateful.
Additionally, I would like to thank my committee members, Dr. Dan Russell and Dr.
Michelle Vigeant for their continued support and advisement through my thesis work.
Next, I want to thank GN Hearing for the opportunity to work on this project as well.
Their desire to collaborate with Penn State on such an innovating subject has been
invaluable to me. The fact that I am associated with such great organization through
this project is incredible.
I would also like to thank the Graduate Program in Acoustics as Penn State for not only
providing me with a fantastic education, but for inviting me into a family. Countless
individuals from the program, faculty, and students alike, have been extremely
thoughtful and helpful in relation to my work on this project. Countless more have been
helpful in even more ways outside the realm of this project.
I would like to offer specific thanks to those who aided significantly in this project’s
development. Lane Miller provided the foundation for this project mentored me so well
during our period of overlap at PSU. Without Lane, this project would not be where it
is today. Additionally, Matthew Neal, Zane Rusk, Jonathan Broyles, and Jason Sammut
provided significant help to various areas of the project.
Lastly, I have to thank Cristina Ochoa. As a fellow acoustics student, you have been
the primary source of second opinions. As my best friend, you have provided comedic
relief during stressful times. And as my soon-to-be wife, you have been and will
continue to be my unwavering support through the highs and lows of life.
1
Chapter 1: Introductory Material
1.1 Project Overview This thesis examines the continued research and development efforts by
Pennsylvania State University’s Transducer Development Laboratory (TDL) to
develop an active noise cancelling system for reducing undesirable noise traveling
through open windows while retaining sufficient air and daylight ventilation.
Previous research from the TDL is covered in a thesis by Lane Miller and is
referenced extensively throughout this paper [18]. Miller’s research focused
primarily on the development of a unique optimization algorithm for obtaining
secondary source beam forming filters using theoretical acoustics and various digital
signal processing techniques. Miller’s research produced simulated noise cancelling
results which exceeded the findings of several published works in the field. Upon
the completion of the theoretical research, the global project objective shifted to
obtaining experimental validation for the simulated results. This has involved
designing, fabricating, and measuring the performance of a secondary source array
to be used in an active noise cancelling system.
The specific work covered in this thesis focuses primarily on the iterative
development of the secondary source array. The array development has seen three
completed iterations. The first iteration was developed entirely by Miller. The
second array was developed by Miller and Downey together. The third iteration was
developed entirely by Downey. Unfortunately, the Covid-19 pandemic severely
limited research productivity, and the noise reduction performance of the third array
iteration was never evaluated. Subsequently, the scope of this thesis has been
narrowed considerably. Despite this setback, significant progress was made toward
the global project objective as substantial improvements were made to the secondary
source array and the measurement facility used for array performance analyses.
2
1.2 History of Active Noise Cancelling Noise pollution has historically been overlooked by society. A wave of awareness
in the 1970s brought about widespread legislature regarding the control of noise
levels throughout the world [20]. Since then, when fighting noise pollution in
workplaces, public spaces, and other loud areas, the primary course of action has
been to decrease the noise through passive attenuation. Passive attenuation refers to
the reduction of sound by means of physically isolating the sound from the desired
quiet location. Examples of passive attenuators include sound barriers along
highways, walls of a house, and rubber tips of in-ear headphones. Unfortunately,
passive attenuation methods often only provide significant attenuation in mid to high
frequency ranges. Additionally, passive attenuation methods have become
increasingly difficult and expensive to implement in urban areas with high-rise
workplaces and homes. Because of the increasing challenges associated with
implementing passive noise reduction systems, researchers have begun pursuing
other noise control solutions.
Active noise control has been a well-documented and understood branch of applied
electro-acoustics but has traditionally been deemed impractical for large scale
implementation. However, with the advent of faster and cheaper technology over
the last 30 years, active noise cancelling (ANC) solutions have continued become a
more realistic possibility for combatting noise pollution [9]. Even more recently,
research has blossomed in the field of large volume active noise control for the
application of ANC systems in office spaces, schools, and even residential areas. As
technology has continued to improve, the goal of creating and implementing
effective ANC systems for large volumes has nearly come within reach.
3
1.3 ANC System Overview
1.2.1 ANC Fundamentals
Active noise control involves increasing or decreasing sound wave amplitudes using
constructive or destructive wave interference. Active noise cancelling refers
specifically to the destructive interference and subsequent reduction of unwanted
sound. The fundamental acoustic property of linear superposition explains that the
destructive wave, or anti-noise, is simply added to the noise such that the
combination results in a decrease in amplitude. For complete noise cancellation, the
destructive sound wave must be an exact replica of the noise and be shifted out of
phase by 180 degrees, or phase inverted. Figure 1 shows this principle using a tonal
signal, or sine wave.
ANC systems have been researched and utilized for various applications over the
last twenty years with the most effective implementation being in headphones. ANC
systems found in headphones typically use several microphones to continuously
record the unwanted noise signal. The recorded signals are then processed in real
time using a series of filters which provide signal shaping and phase inversion. This
filtered signal is then played through the primary headphone speakers. Using these
methods, recently developed consumer headphones provide upwards of 25 dB of
Figure 1: This diagram shows an ideal noise cancellation scenario for a pure tone signal. [18]
4
reduction at low frequencies (100-500 Hz) [8]. Because of the commercial success
of ANC headphones in recent years, ANC systems have become nearly essential for
headphones to be considered high-quality. A diagram showing a typical ANC
system for headphones is shown in Fig. 2.
1.2.2 Large Volume ANC
From the well-understood headphone application, this project seeks to apply the
same concepts and technology to reduce sound coming through open windows. One
specific example would be traffic noise in an urban area coming through an open
office window. The office interior is analogous to the ear interior of an ANC
headphone user. The goal of using a large volume ANC system would be to cancel
the sound within the entire office interior, as the goal for headphones is to cancel
the sound within the ear canal. The main difference in application is the size of an
office verses the size of an ear canal. There are acoustic challenges that arise when
applying ANC to large volumes that are not present in the smaller volumes
associated with headphones. These challenges have led past researchers to consider
such ANC systems impractical to implement if not outright impossible [11].
Over the last ten years, innovations in technology, specifically, the development of
more efficient digital signal processing abilities and the decrease in cost for ANC
system components have led to a surge in motivation and research in the area of
Figure 2: The noise signal would be continuously recorded by the feedforward and feedback microphones. The signals would then be filtered using a digital signal processing chip. After processing, the anti-noise signal is played through the same speaker used for general audio listening. The result is localized noise reduction inside the ear canal.
5
large volume active noise control. Some early ideas included providing localized
cancellation in small zones, such as around an individual’s headspace, within large
volumes like office spaces [25] and airplanes [3]. This method utilizes microphones
and speakers oriented around the specific zone of interest. The problem with this
approach is that while it may provide a small region of quality noise reduction,
regions outside of that location often experience constructive interference. At times,
this results in the sound levels being significantly higher than if no ANC system was
present at all. Also, to provide cancellation with this method for several people, each
individual would require a unique ANC system. The cost of implementing so many
systems would not be a cost-effective solution for office spaces.
While some researchers are still looking at this type of approach, many have shifted
to studying global ANC systems. Global cancellation implies the reduction of noise
throughout the entirety of the volume of interest. To achieve this, the ANC system
must be implemented at the primary entrance point of the sound into the room. For
the case of an office with open windows, the ANC systems would be implemented
at the windows. This approach can be seen implemented by various leaders in this
research area [24], [14], [27]. While many groups are actively researching the
general concept of global ANC systems for large volumes, there are some key
differences to the approaches being taken.
To understand the differences among the various global cancellation techniques
being implemented, there must be a fundamental understanding of how the ANC
systems function. First, the noise signal originates and impinges on the window. An
ANC system has some number of microphones outside the window which receive
the noise signal. This signal is filtered using a control system and is sent to an array
of speakers termed a secondary source array. The array then plays the anti-noise
signal into the interior volume. Then, depending on the processing capabilities of
the system, there may be a feedback system to optimize the cancellation. The
feedback portion of the control system would include some number of error
microphones inside the volume. These error microphones capture the residual noise
and send this signal back into the system for further filtering. The feedback system
6
operates in conjunction with the feedforward system to improve total effectiveness
of the system. One may understand this to mean that the feedback system works to
reduce any leftover noise that the feed forward system was unable to cancel. Figure
3 represents this type of window ANC system.
In the figure, the secondary sources are generating the anti-noise signal into the
volume where the cancellation is desired. Thus, the destructive interference is
occurring throughout the entirety of the volume’s interior. The error microphones
would then be strategically placed on the volume interior to measure the remaining
noise. While the diagram shows only one microphone on the exterior and interior,
systems often have several feedforward and feedback microphones. From observing
the diagram, one begins to gain an appreciation for the processing power and speed
required to operate a large volume ANC system. Simultaneous recording and
playback must occur with many microphones and speakers, and the control systems
require real time filtering. Without the recent advancement of computational tools,
these systems would be practically impossible to implement.
Figure 3: The noise signals are captured using the two types of microphones, filtered and phase inverted using the control systems, and introduced into the room at the noise source (window) to globally reduce the noise levels inside the room.
7
1.2.3 ANC Performance vs. Ventilation
One of the primary challenges associated with developing a practical ANC system
for open windows is determining the balance between window functionality and
ANC performance. For the application of office spaces, businesses often desire the
benefits of both natural ventilation and daylight from windows and a quieter office
environment. Researchers have struggled to find an effective way to optimize ANC
systems and provide both deliverables.
Research groups with a heavier emphasis on maintaining ventilation have attempted
developing an array of secondary sources distributed only around the outside of the
window frame [5,12,24]. This type of array is termed an edge-distributed array and
allows for complete ventilation. These research groups performed both theoretically
simulated and physical measurements. While the ANC systems provided excellent
ventilation, moderate noise cancellation was measured only at lower frequencies.
Other research groups focusing on maximizing the ANC performance, like the
research group at Nanyang Technical University (NTU), have developed systems
where the secondary sources are dispersed evenly throughout the plane of the
window. This type of array is termed a distributed array. In simulated testing
performed at NTU, distributed arrays provided significantly better noise
cancellation than edge distributed arrays [16]. Additionally, the NTU research group
was able to experimentally validate some of these theoretical results [17], however,
the distributed array used naturally occluded a significant portion of the window and
reduced ventilation. The conclusions drawn from the various leading researchers
differ based on what deliverable was deemed more valuable and what array type
was used. Figure 4 provides visualization for both array types.
8
Despite the differing conclusions from researchers on which array type was best, the
theoretical simulations performed all show that distributed arrays provided the best
noise cancellation performance and the worst ventilation. Conversely, the edge-
distributed arrays provided the worst noise cancellation and the best ventilation [13,
24]. The natural next step in the research and design process was to find a way to
optimize the ventilation and ANC performance to arrive at some best-case ANC
system design. Ideally, this design would have similar ANC results in comparison
to the distributed array with better ventilation characteristics.
1.3 PSU Research
1.3.1 Sparse Arrays and Beam Forming
An array that attempts to capitalize on the benefits of both array types has been
developed by Penn State’s TDL and termed a “sparse array.” A sparse array utilizes
an edge-distribution with a partial, symmetric distribution of array elements within
the window plane. The sparseness, or density, of the array elements determines the
ventilation and performance abilities of the noise cancelling system. Finding the
ideal balance between the two types of systems was the ultimate design
consideration for this work. The optimal array geometry determined through
Miller’s work was a four-cell sparse array where “cell” refers to the number of
distinct openings on the array [18]. This array geometry is illustrated in Fig. 5.
Figure 4: The left array shows the speaker layout for an edge-distributed array while the right shows that for a distributed array.
9
Miller developed a numerical model to compare the ANC performance of the three
array types discussed thus far. As expected from the results of other researchers,
Miller’s results showed that distributed arrays outperform both sparse and edge-
distributed arrays. Accordingly, sparse arrays outperform edge-distributed arrays
[18]. From analyzing these ANC performance differences, the general observation
was concluded that having more speakers throughout an array would increase its
noise cancelling performance. This conclusion led to an in-depth investigation of
spatial sampling, which is a fundamental obstacle for large volume ANC.
When sound impinges on a window, the waves bend in certain patterns around the
opening due to diffraction. Instead of being simplified to one-dimensional plane
waves, as can be done with ANC headphones, sound waves in large volumes must
be understood to propagate as three-dimensional beams. Because linear
superposition still applies, the primary goal of large volume ANC is to replicate the
noise’s entire three-dimensional beam pattern using the secondary source array. If
the beam patterns are identical in shape and phase inverted, the added result will be
no net sound. An example of such a beam pattern is shown in Fig. 6.
Figure 5: The sparse array consists of a grid of four squares with speakers distributed along the grid lines. This layout combines edge-distributed and distributed designs into a more optimal geometry.
10
The number of speakers and their distributed locations throughout an array
determines how well the sound field is spatially sampled and how well the array can
replicate the noise beam pattern. Spatial sampling is analogous to digital sampling,
implying that a higher spatial sampling would result in a more accurate replication
of the noise beam pattern. For an array with infinitely many speakers throughout the
window opening, the noise beam pattern would be perfectly spatially sampled and
would be perfectly replicated by the array. For an array with only one speaker in the
opening, the noise beam pattern would be poorly spatially sampled and would be
poorly replicated by the array. More simply stated, using more secondary sources in
the window opening increases the spatial sampling, and thus improves the beam
pattern replication.
When attempting to replicate beam patterns at higher frequencies, if the spatial
sampling is too low, the array will encounter spatial aliasing problems. In relation
to temporal aliasing, spatial aliasing causes the beam pattern replication to begin
failing at a certain frequency. With this considered, to effectively implement an
ANC system over a specific frequency range, the spatial sampling of the array must
be high enough to accurately replicate the beam pattern produced by the noise at the
upper frequency bound.
Figure 6: The balloon-like figure is a MATLAB generated theoretical beam pattern which represents the sound field generated when plane waves impinge on a rectangular opening. [18]
11
The beam pattern shaping is performed by prescribing unique magnitude and phase
values at each frequency to the drivers in the array. Essentially, unique filters are
applied to each speaker such that the total array beam pattern can be formed, or
steered, into a desired shape. Beam forming and array steering are well established
methods for shaping sound waves and the theory is discussed in more detail by
Beranek and Mellow [2]. When beam forming is used in conjunction with a higher
spatially sampled array, the ANC results are improved significantly. This
improvement implies that a distributed array with beam forming applied would
outperform the sparse array with beam forming. However, a distributed array
without beam forming applied may not significantly outperform a sparse array with
beam forming applied. At this point, revisiting the primary goal of using a sparse
array with beam forming is necessary.
The goal of using beam forming with a sparse array was to provide noise
cancellation comparable to the distributed array while providing better ventilation.
Penn State’s TDL hypothesized that this was feasible assuming the beam forming
provided a significant improvement to the ANC performance. This approach
continues to appear unique when compared to other published methods.
1.3.2 Optimization Overview
Miller’s most significant contribution to TDL’s research was developing an
optimization algorithm which determined the beam forming filters for the drivers in
the sparse array. The algorithm computed the magnitudes and phases which
optimized the ANC performance of the array. This optimization involved computing
the complex pressure fields for both the noise and anti-noise and minimized the
difference between those values at each frequency. The following text is a general
overview of the algorithm and acoustic computations involved. The optimization
algorithm and acoustics derivations are discussed in more depth in Miller’s thesis
[18].
12
The noise pressure field was assumed to be a plane wave encountering a rectangular
opening. For sound passing through a rectangular opening, the far-field radiation
was modeled as an oscillating piston with a uniform surface velocity. Figure 7 shows
a model of this type of sound field with the velocity profile, k-space profile, and
directivity, or beam pattern.
Theory for sound radiation from a rectangular opening is well understood, and the
derivation of the pressure distribution was covered thoroughly in Miller’s thesis
[18]. The resulting normalized pressure is shown along with the directivity in
equations 1 and 2, where L and k represent length and wavenumber respectively
𝑝𝑝𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 =𝑗𝑗𝑗𝑗𝜌𝜌0
2𝜋𝜋𝑒𝑒−𝑗𝑗𝑗𝑗𝑗𝑗
𝑟𝑟 𝐿𝐿𝑥𝑥𝐿𝐿𝑦𝑦sinc �𝑘𝑘𝑥𝑥𝐿𝐿𝑥𝑥
2 � sinc�𝑘𝑘𝑦𝑦𝐿𝐿𝑦𝑦
2 � [1]
𝐷𝐷𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 𝐿𝐿𝑥𝑥𝐿𝐿𝑦𝑦sinc �𝑘𝑘𝑥𝑥𝐿𝐿𝑥𝑥
2 � sinc �𝑘𝑘𝑦𝑦𝐿𝐿𝑦𝑦
2 � . [2]
The next step was to model the anti-noise sound field produced by the sparse array.
The pressure radiated is the combined pressure field of all the speakers in the array.
Because of the relatively low frequency range of operation and small size, the
individual speakers were assumed to behave as point sources, or monopoles. The
pressure radiated by a single monopole at an instant in time is given in equation 3
𝑝𝑝𝑚𝑚𝑛𝑛𝑛𝑛𝑛𝑛 =𝑗𝑗𝑗𝑗𝜌𝜌0𝑄𝑄
2𝜋𝜋𝜋𝜋 𝑒𝑒−𝑗𝑗𝑗𝑗𝑗𝑗 . [3]
Figure 7: From left to right, the figure shows a uniform velocity profile, k-space Fourier transform, and directivity pattern of a plane wave interacting with a large rectangular opening. [22]
13
Linear superposition allowed the total pressure field to be approximated as a
summation of point sources. Equation 4,
𝑝𝑝𝑎𝑎𝑛𝑛𝑎𝑎𝑛𝑛 = 𝑗𝑗𝑗𝑗𝜌𝜌0𝑄𝑄
2𝜋𝜋 �𝑒𝑒−𝑗𝑗𝑗𝑗𝑗𝑗𝑖𝑖𝜋𝜋𝑛𝑛
𝑁𝑁
𝑛𝑛=1
, [4]
shows the impact of the source locations relative to an arbitrary observation point
for each driver, distances Ri. In the optimization algorithm, the only array specific
input necessary was the driver locations. Meaning that if the array geometry was
known, the optimized filters could be computed. The total radiated pressure,
𝑝𝑝𝑎𝑎𝑛𝑛𝑎𝑎𝑛𝑛 = 𝑗𝑗𝑗𝑗𝜌𝜌0𝑄𝑄
2𝜋𝜋𝜋𝜋𝑒𝑒−𝑗𝑗𝑗𝑗𝑗𝑗𝑟𝑟𝑟𝑟𝑗𝑗
�𝑒𝑒𝑗𝑗𝑗𝑗𝑥𝑥𝑠𝑠,𝑖𝑖 sin(𝜃𝜃)cos (𝜙𝜙)𝑒𝑒𝑗𝑗𝑗𝑗𝑦𝑦𝑠𝑠,𝑖𝑖 sin(𝜃𝜃)sin (𝜙𝜙)𝑁𝑁
𝑛𝑛=1
, [5]
is expressed spatially in terms of locations Ri and in spherical coordinates in
equation 5. The directivity is also given in spherical coordinates in equation 6
𝐷𝐷𝑎𝑎𝑛𝑛𝑎𝑎𝑛𝑛 = �𝑒𝑒𝑗𝑗𝑗𝑗𝑥𝑥𝑠𝑠,𝑖𝑖𝑒𝑒𝑗𝑗𝑗𝑗𝑦𝑦𝑠𝑠,𝑖𝑖
𝑁𝑁
𝑛𝑛=1
. [6]
Miller’s algorithm computed both radiated pressures from equations 1 and 5 and
computed the difference between the two as shown in equation 7 [18]
𝑝𝑝𝑑𝑑𝑛𝑛𝑑𝑑𝑑𝑑 = 𝑝𝑝𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 − 𝑝𝑝𝑎𝑎𝑛𝑛𝑎𝑎𝑛𝑛 . [7]
This difference equation was the objective function minimized in the algorithm.
When 𝑝𝑝𝑑𝑑𝑛𝑛𝑑𝑑𝑑𝑑 was minimized, the algorithm reached an optimal solution, and the
magnitudes and phases were output.
1.3.3 Simulated Results
The results of Miller’s simulations revealed the frequency dependency of the beam
forming performance in relation to the array geometry, the amount of sound
reduction possible using a sparse array geometry, and the array’s theoretical ANC
14
performance compared to other researchers’ results [18].
As discussed previously, the highest frequency of significant noise cancellation was
limited by the spatial sampling. Miller’s theoretical results showed that, for the
sparse array with beam forming, significant cancellation (at least 10 dB) up to
around 1500 Hz was possible. Based on Miller’s findings and other researchers’
conclusions, the targeted frequency range of operation using a sparse array was
determined to be 300-1500 Hz.
Additionally, Miller’s simulation results showed that below 1000 Hz, noise
cancellation over 100 dB was possible, implying near perfect beam pattern matches.
Above 1000 Hz, the cancellation performance declined quickly, and the region of
significant cancellation ended near the 1500 Hz bound [18]. Figure 8 shows Miller’s
simulated beam patterns for the noise and anti-noise signals up to 1200 Hz using the
equations discussed previously. The figure shows nearly identical matches for the
beam patterns, and the amount of reduction associated with each frequency is given.
The figure also shows that as the frequency increases, the beam patterns develop
side lobes. At 1200 Hz, four side lobes are quite prominent. As the beam patterns
become more complex with even more side lobes (>1500 Hz), replicating the sound
field becomes increasingly more challenging for the sparse array. At these high
frequencies, the total beam pattern of the anti-noise bears little resemblance to the
noise and little to no cancellation occurs.
15
When comparing these simulations to results from other researchers in the field, a
sparse array with beam forming theoretically performed as well or better than other
array simulations up to the frequency limit [10, 24, 14]. Because other researchers’
simulations did not include the same filtering technique, beam forming was
concluded to increase ANC performance significantly in theory.
Overall, while the limited spatial sampling restricted the maximum frequency of
noise reduction, the amount of cancellation in the operable frequency range
increased considerably when using the unique beam forming filters. With the
simulations completed, the next step in the research process was to build a physical
ANC system with a sparse array and implement the beam forming filters to attempt
validating the simulated results with experimental results.
Figure 8: The theoretical beam patterns for the noise and anti-noise pressure fields are compared. Miller’s theoretical simulations showed near perfect cancellation results were possible using a sparse array up to 1200 Hz. [18]
16
Chapter 2: Experimental Design Overview
2.1 Generic Experimental Method Performing acoustical measurements of large volume ANC systems is a challenging
task. A complete ANC system includes primary sources, feedforward reference
microphones, secondary sources, and feedback error microphones all operated by a
digital controlling system. This is shown in the diagram in Fig. 9 and is a condensed
version of Fig. 3.
If any of the subsystems are not operating correctly, the ANC measurement data
may be misleading or, in the worst case, completely invalid. Problems could be as
small as one distorting speaker in the entire secondary source array. Additionally,
other non-acoustical factors contribute to the validity of ANC measurement results
including measurement environment and mechanical design. For optimal
experimental testing, the entire ANC system would be contained in an acoustically
anechoic facility. Using a free-field measurement environment would alleviate any
Figure 9: Generic experimental ANC design with elements similar to those shown in Figs. 2 and 3. [18]
17
challenges associated with reflected sound waves. The system should also be well
isolated from noisy environments to avoid the introduction of fraudulent data. The
mechanical design could also contain various issues which contribute to misleading
ANC results. For example, structural vibrations or poorly mounted speakers could
corrupt measured data.
The plethora of design considerations present for a large volume ANC system
reveals numerous potential challenges associated with obtaining valid ANC
measurement data. In order to validate the theoretical results, careful consideration
must be made to minimize potential measurement errors in every part of the system.
2.2 External Experimental Methods The amount of available documented experimental research is limited, and while the
generic process is well understood, the specific design of each facet of the ANC
system varies among researchers. Variations in methodology can at times be traced
to limitations in the resources needed to develop an entire ANC system and perform
ideal ANC measurements. Some possible limitations include the lack of sufficient
lab space [14], lack of funds available for purchasing measurement equipment, lack
the educational background needed for each subsystem design, or lack of labor
needed to efficiently develop the entire system. Because of the general lack of
previous research and these various limitations, the researchers having attempted
experimental validation have used considerably different design methods and have
achieved generally differing results. Results are shown in TBL. 1 for several
research groups, referenced previously, who have performed experimental
measurements [16].
18
The table is fairly comprehensive and covers many of the published experimental
results. When reviewing the table, inconsistencies in the experimental designs used
were noticed. Whether the difference be the array configuration, noise source signal,
or window size, the experiments varied significantly. The only somewhat consistent
observation made was that for those attempting global cancellation, distributed
arrays provided more reduction on average than edge-distributed arrays. This
aligned with conclusions derived from the analysis of spatial sampling and many of
the researchers’ numerical solutions. However, in cases like the 2017 study by Wang
[27], the distributed and edge-distributed arrays performed similarly, and this was
the only case where the experiments were performed identically aside from array
geometry. A better conclusion from this table may be that there were simply not
enough experimental results documented to arrive at any definitive conclusions. The
limited amount of separate measurements and inconsistency in methodology used
highlighted the challenges of obtaining consistent experimental results. Still, some
of the experimental results listed above were encouraging.
More recently, the research group at NTU published the most legitimate
experimental validation for large volume ANC systems to date. The group was able
to develop an ANC system which consistently provided up to 10 dB of global noise
reduction over a broad band (400-1000 Hz) frequency range [17]. The array used
was distributed and provided sufficient air ventilation but only moderate daylight
ventilation. While minimal in design for a distributed array, the array still occluded
Table 1: The chart covers a range of experimental results from various ANC measurement methods. Note that some results seem to share similarities with Miller’s simulations, where reduction upwards of 15 dB had been measured between 500-2000 Hz. Note that the references in the table do NOT correspond to references in this paper.[16]
19
most of the window opening. The success of this experimentation was enormous for
the prospective commercial interest in large volume ANC systems. Even so, the
design would be significantly improved with increased ventilation. The PSU TDL
believes that the NTU array’s combined ANC and ventilation capabilities can be
improved upon using a sparse array with applied beam forming filters.
2.3 Internal Experimental Methods This section provides a brief review of this project’s initial experimental methods
and array design which laid the foundation for project’s future.
2.3.1 Methodology
After Miller’s theoretical modelling was deemed sufficient, a unique experimental
methodology was developed. With the primary focus being the application of the
beam forming filters, the experimentation focused primarily on the secondary source
array. The beam forming evaluations were conducted without integrating the
feedforward and feedback control systems. By minimizing the amount of processing
involved, the effectiveness of the beam forming filters could be isolated and
analyzed without regard for the effectiveness of the control system. Simply put, with
fewer variables, the impact of beam forming could be analyzed more directly. This
experimental procedure involved less hardware and software than a fully integrated
ANC system. The reduced ANC system implemented only a primary noise source,
secondary source array, measurement microphones, and simplified control system
consisting of an audio interface and laptop computer. A diagram of this simplified
experimental approach is shown in Fig. 10.
20
Rather than including a feedforward microphone system to predict the sound field,
the noise source is placed a known distance away from the secondary source array.
By accounting for the time of flight delay from the primary source to secondary
source array, the array is told to begin playing the anti-noise at the precise moment
when the noise arrives at the window. This method assumes that the spherical sound
wave from the primary source may be approximated as a plane wave when it reaches
the array. The equations used to compute the time delay are
where d is the distance from the noise source to the array, c is the speed of sound,
and T is the ambient temperature of air in the room.
Removing the feedforward and feedback systems yielded a system with minimal
real-time signal processing necessary. The reduction in computational burden on the
control system allowed for the usage of less powerful machines as controlling
devices.
𝑡𝑡𝑑𝑑𝑛𝑛𝑑𝑑𝑎𝑎𝑦𝑦 =𝑑𝑑𝑐𝑐 [8]
𝑐𝑐 = 331.6 + 0.61𝑇𝑇, [9]
Figure 10: The reduced experimental design was developed specifically to analyze the effectiveness of the beam filtered secondary source array. The control system would prescribe audio signals to the primary and secondary sources while a separate control system recorded the resultant audio data.
21
2.3.2 Measurement Facility
The initial measurement environment for the experimentation included an anechoic
chamber coupled to a reverberant chamber via a transmission window. A diagram
of the facility is shown in Fig. 11.
While the notion of having two rooms coupled together by a window-like opening
seemed promising, several challenges arose while using this measurement facility.
Acoustically, the ideal facility would include two anechoic chambers coupled
together by a transmission window. When analyzing global ANC reduction, sound
level measurements would ideally be taken at many locations throughout the
receiving room. For example, one measurement system used by NTU included 27
measurement microphones distributed throughout the receiving room [16]. This
ensured that noise cancellation was occurring at all locations throughout the space.
To ensure accuracy in the results, measuring only the direct path sound waves is
desirable. Reflections cause the pressure levels at microphones, especially those
near walls or corners, to be artificially increased or decreased because of sound wave
interference. Because of this, using the reverberant chamber as the receiving room
was a poor choice. Figure 12 depicts this issue. In the figure, the blue microphone
location allows for clear distinction between the direct path sound and any
Figure 11: The diagram above comes from a research thesis by Paul Bauch [1] and gives a dimensioned, 3-D perspective of the measurement facility used. The circle shows the window used for transmission between the rooms. Note that this figure shows the chamber prior to a 2012 remodel which saw some minor geometry changes.
22
reflections which occur. The green and red microphone locations, however, both
have numerous reflections which would arrive nearly simultaneously with the direct
sound. Because of this, using the reverberant chamber as the receiving room was
later abandoned.
Knowing this, the other measurement option would be to use the reverberant room
as the source room and the anechoic chamber as the receiving room. However, this
design choice would be even worse because of impact of reflections on the noise
signal. Without feedforward microphones, knowing the exact noise signal generated
by the primary source is essential for accurate beam shape reproduction. Using the
reverberant chamber as the source room would introduce reflections to the known
noise signal which would not be accounted for in the beam forming filters applied
to the secondary source array. The addition of reflected noise signals would likely
result in poor noise reduction. While a non-ideal choice for both receiving and
source rooms, the reverberant chamber was used as the receiving room; thus, serving
as the better of two poor measurement design choices.
An additional challenge associated with using this measurement facility was the
inability to access the space when needed. The anechoic chamber was operated
Figure 12: The figure shows an example of how reflections can cause challenges when performing acoustic measurements. While the reverberation time was never officially measured, it was generally estimated to be 4-6 seconds.
23
largely by a separate acoustics research group for significantly different work. This
meant that the TDL had to schedule around the availability of the group operating
the facility. Additionally, because of the nature of the other lab’s work, a significant
amount of disassembly was required to even access the reverberant chamber and
transmission window. Because of these restrictions, any amount of experimentation
done by the TDL needed to occur over a relatively short time window. This allowed
little room for troubleshooting during measurements, and if erroneous data were
observed after experimentation was completed, remeasuring would require going
through the entire setup process again. While only logistical in nature, this issue
prevented the TDL from being able to perform measurements efficiently.
Despite these challenges, this measurement facility was utilized for the first two
iterations of ANC testing. While far from ideal, the coupled chamber unit was the
best available option for performing the necessary measurements at the time. Once
the general measurement process and testing environment were established,
designing the array became the project focus.
2.3.3 Array Iteration 1: Design
The focal point of the experimental design was the secondary source array. The array
design consisted of a rigid frame on which speakers were mounted. Some array
design considerations included the acoustic performance of speakers, frame
construction, and speaker attachment method.
In the first array built by Miller, the speakers used were small, Dayton Audio
CE32A-4, drivers (1.25 in.). Using smaller drivers permitted Miller to use more
speakers in the sparse array geometry. With more speakers in the array, a more
thorough spatial sampling of the window was achieved. The speakers were arranged
in groups of six and were mounted as line arrays in plastic, 3-D printed units. One
of these units is shown in Fig 13. Within each line array unit, each driver had a
unique closed-box baffle and wiring set. The array consisted of 12 of these speaker
boxes, thus leading to 72 total speakers [18].
24
Miller constructed the sparse array frame using plywood and hand tools. When the
frame was constructed, the speaker boxes were mounted to the frame using Velcro.
An image of the fully constructed array is shown in Fig. 14.
Figure 13: The line array above was one of 12 units installed in the first iteration of the array design. [18]
Figure 14: The image shows the first array iteration installed in the transmission window of the coupled chambers. In this measurement setup, the anechoic chamber visible through the window is the source room, while the reverberant chamber is the receiving room. [18]
25
2.3.4 Array Iteration 1: Experimental Testing
Performing measurements using the sparse array discussed above required several
pieces of equipment in the signal chain. First, a controlling laptop computer was
used to generate and send the desired audio signals to each speaker in the array using
MATLAB. The computer was connected to three, 24-channel MOTU output
devices. The individual outputs from the MOTU devices were then run through
Dayton amplifiers to increase the signal amplitudes for each driver. Using this
method, each driver was able to be individually controlled from the computer.
The first measurements involved obtaining the frequency responses of each driver.
To maximize the ANC effectiveness, the frequency responses of all drivers needed
to be as similar as possible to provide a consistent baseline for beam forming filters.
This process involved measuring the natural frequency response of each driver, then
applying an equalization filter to each driver to smooth and unify the responses. The
development and implementation of this process is discussed in more detail in
section 3.2.1.
The next measurement was to evaluate the array’s beam forming capabilities
compared to the predicted results from the numerical solutions. Miller performed
directivity tests to analyze the effectiveness of the beam pattern filters applied to the
array. Unfortunately, several problems arose during this testing and the measured
beam patterns from the array did not match the theoretical results as well as
expected. Figure 15 shows some of these results.
26
Several potential sources of error were observed during this measurement. Namely,
the beam forming filters applied high gain levels at certain frequencies. These
drivers, being rather small, suffered from significant harmonic distortion problems,
particularly at lower frequencies. A speaker’s harmonic distortion in relation to its
size is well understood and is discussed at length in an overview of speaker
distortion by Klippel [13]. When later attempting actual noise cancellation
measurements with this array, Miller found that while the array did cancel some
sound, the harmonic noise generated by transducer distortion was audibly present
and corrupted the measurements. This problem rendered the array ineffective.
Additionally, the mounting method for the drivers was not robust enough. Using
Velcro was not a rigid fastening solution, and the speaker boxes, while moderately
constrained, were able to wobble slightly. If the speakers were pointing slightly off
axis, the beam patterns would have become slightly warped from the intended beam
shape. Despite the ease of setup associated with using the Velcro, the lack of
Figure 15: Theoretical and experimental directivity patterns are compared at specific frequencies. In some instances, such as the 400 and 1100 Hz plots, the array beam pattern matched the theoretical pattern fairly well. However, other examples, such as the 700 and 1000 Hz plots, show poor matching. [18]
27
robustness and potential errors associated with this mounting method were too high
to continue using it.
Along with the above problems, some digital control issues were present during
these measurements. Miller dealt with various latency issues associated with the
control system. While using a simplified ANC model without feedforward and
feedback systems eased the signal processing load to an extent, the use of three
interfaces and 72 drivers through one controlling computer still generated latency
issues. Additionally, Miller used MATLAB as the controlling software, which has
historically been a sub-standard audio interfacing software. Knowing this, some of
the latency issues may have also been associated with the software choice.
After experimentation using first array iteration was completed, the necessary
design improvements were reviewed. First, the second iteration required higher
performing speakers at a lower quantity. The lower number of drivers would lead to
less digital signal processing problems and implementing higher performance
drivers would result in improved acoustic performance with less distortion.
Additionally, the method used for mounting the drivers to the array frame would be
altered to something more robust. These design changes are addressed fully in the
following chapter.
28
Chapter 3: Array Iteration 2
3.1 Design In the previous chapter, the original sparse array was discussed, and its shortcomings
were revealed. The second sparse array design sought to rectify the errors discussed
previously. Additionally, the primary focus of the project had officially shifted from
including some theoretical acoustics to entirely experimental acoustics. With this
shift came a more thorough consideration of the mechanical design of the array and
the performance of the secondary source transducers.
3.1.1 Transducers
The first step to improving the acoustic performance of the array was to exchange
the transducers used in the first array with higher quality drivers. A search was
conducted for new drivers with two main characteristics: a flat magnitude response
in the frequency range of operation (300-1500 Hz) and low harmonic distortion.
Finding speakers claiming to have a relatively flat response was not challenging.
Additionally, rather than searching for drivers with less distortion at the same size
as the original drivers, the new drivers were permitted to be larger in size. This
would naturally lessen some of the distortion problems present at low frequencies
because larger speakers produce a greater low frequency output than smaller
speakers for a given signal amplitude. By using larger speakers, spatial constraints
required fewer total speakers be used in the array. With this change, the design goals
of improving acoustic performance and alleviation of digital signal processing load
were mutually inclusive. In order to maintain relatively large openings for
ventilation, smaller sized drivers were considered for interior drivers while larger
sizes were considered for the exterior drivers. Ultimately, two different drivers were
chosen for the array which were distributed as 12 exterior and 9 interior drivers.
29
The loudspeakers used in the second array design are shown in Fig. 16. The exterior
drivers were Dayton ND-91-8 models and were 3.5 inches in diameter. The interior
drivers were Tang Band W2121s models and were 1.75 inches in diameter. The
decision to use different sized speakers required an increased size constraint of the
interior driver mounting surface. The choice of a 1.75-inch interior driver
constrained the frame crossbar on which the drivers were mounted to be at least 2
inches.
Images of the frequency responses provided in the specification sheets are shown in
Figs. 17 and 18. The frequency range of interest is denoted by the red lines on the
figures. Full specification sheets are given in Appendix A.
Figure 16: The driver to the left is the 3.5-inch Dayton ND91-8 which was used on the exterior of the array. The driver to the right is a 1.75-inch Tang Band W2121s which was used on the interior of the array.
Figure 17: The specified frequency response of the Dayton ND91-8 driver is shown above and is fairly flat in the frequency range of operation.
https://www.parts-express.com/
30
The frequency responses for both loudspeakers showed less than 5 dB of variation
in the frequency range of interest. The smaller, Tang Band drivers appeared to have
slightly more variation, but both seemed flat enough in the frequency region of
operation to be equalized easily.
3.1.2 Mechanical Design
The first step to improving the mechanical design of the array was to improve the
efficiency and repeatability of the array construction. To do this, by-hand
construction was abandoned in favor of precision machining. The construction was
outsourced to the Penn State University Stuckeman School of Architecture DigiFab
lab. This lab was capable of large-scale computer numerical control (CNC) routing
for a selection of woods, and medium-density fiberboard (MDF) was chosen as the
construction material for the array frame. This material selection changed the array
design from plywood to MDF. Along with this design change, the array frame
thickness was decreased from ¾-inch to ½-inch. While some consideration went
into these changes, no significant structural analysis was performed.
The material selection was based primarily on ease of machining. For the CNC
process, MDF was both the easiest and least expensive wooden material available
for machining in the Architecture lab. The frame thickness was decreased to saved
money on material for construction. Additionally, decreasing the thickness was
thought to improve the accuracy of the baffled piston assumption used in the
Figure 18: The Tang Band W2121s frequency response, shown above in red, has more variability than the Dayton driver’s frequency response.
31
theoretical model of the noise pressure field. The infinite baffle approximation
assumes no flow impedance caused by the edges of the array opening. By decreasing
the frame thickness, the likely minimal fluid flow impacts due to friction on the
interior frame edges were reduced [19].
Another mechanical improvement was that the fine tolerancing capabilities of the
router aided in the implementation of larger interior drivers. To maintain the
structural integrity of the array frame, the interior drivers were limited in size to 1.75
inches, leaving 0.125 inches of framing material on each side of the mounting holes.
Without the precision cutting of the router available, the drivers may have been
limited to a smaller size. The array frame model was sketched and dimensioned
using AutoCAD. A dimensioned array frame drawing and the cut iteration 2 array
frame are shown in Figs. 19 and 20, respectively.
Figure 19: The drawing above was used to program the CNC router used for the array machining. Using the router allowed for much finer detail in the cuts and more consistency for future array iterations. The dimensions are given in inches.
32
The new machining significantly improved the ability to mount the drivers to the
array. The speakers were now able to be mounted rigidly to the frame, and any errors
associated with the previous use of Velcro as the mounting method were alleviated.
The interior speakers fit snugly into the cut holes using only a press fit, but glue was
added to further secure the speakers into the frame and to create an airtight seal
between the fronts and backs of the drivers. The exterior speakers were rigidly
mounted using four screws and were sealed by compressing a rubber ring between
the driver frame and array frame. An image of the array with the speakers mounted
to the frame is shown in Fig. 21.
Figure 20: All speaker holes were cut by the CNC router to be the exact sizes necessary to fit the selected drivers. The blue circle highlights the finely cut interior driver mounting holes.
33
Upon completing the speaker installation, the array was ready for performance
evaluation. An important note here is that the array speakers did not have individual
closed-box baffles as the speakers in iteration 1 had. These drivers were assumed
small enough and baffled enough to perform as monopole sources in the frequency
range of interest. While the addition of enclosures to the speakers would further
ensure the validity of the monopole assumption [2], adding the closed-box baffles
was deemed unnecessary for this application.
3.2 Measurements The acoustic performance of the second array was evaluated by measuring the
frequency responses of the individual drivers. Comparing these results to the
responses on the specification sheets revealed several discrepancies. The measured
results revealed the inadequacy of some of the assumptions made about the array.
After frequency response measurements were taken, ANC measurements were
attempted using this array. These measurements revealed some structural problems
with the array frame which interfered with the results. Both measurement methods
and results are discussed next.
Figure 21: The exterior drivers were fastened to the array using four screws displayed in the figure using red circles. The interior drivers were press fit into the holes and glued in place. The glue was placed along the circumference of the drivers as shown with the blue circle.
34
3.2.1 Frequency Response Measurement Method
Knowing the acoustic behavior of the speakers was vital to understanding and
manipulating the performance of array. Measuring the total array frequency
response involved examining the individual responses of each speaker. With quality
individual responses, the goal was then to equalize each frequency response to be
flat, smooth, and similar to all other drivers, particularly in the frequency range of
interest. If the drivers were well equalized, the application of the beam forming
filters would be significantly more accurate and repeatable.
Measuring the frequency responses of the speakers was conceptually simple. The
process involved playing an excitation signal through the measured speaker and
recording the output signal through a microphone as shown in Fig. 22. Using the
input and output signals, the complex transfer function, or frequency response, was
computed. This is a well-known digital signal processing technique for finding the
transfer function of a system [10]. For this system, the transfer function is essentially
a filter defined by the speaker characteristics. If the input signal is a defined signal
comprised of pure tones, and the speaker acts as a filter, then the measured output
is understood to be the filtered input signal.
When measured, the input signal sent to the speaker and the output signal recorded
by the microphone are both time domain quantities. The transfer function of the
system is defined in the frequency domain. To compute the transfer function, the
input and output signals first need to be translated to the frequency domain. To do
this, the Fourier Transform is applied to both time domain signals. The Fourier
Transform is
Figure 22: The figure provides a visual representation of the input-output system used to define the transfer function of the measured speaker.
35
𝑋𝑋(𝑓𝑓) = ∫ 𝑥𝑥(𝑡𝑡)𝑒𝑒−𝑗𝑗2𝜋𝜋𝑑𝑑𝑎𝑎𝑑𝑑𝑡𝑡∞−∞ . [10]
The relationships between the input and output of the system and between the time
and frequency domains are displayed in Fig. 23. The fast forward and inverse
Fourier Transforms were used to perform the digital domain translations and are
shown as FFT and IFFT.
Once the FFT was applied to the input and output signals, the transfer function was
computed via point-by-point division
There, Y indicates the output signal and X represents the input signal, both in the
frequency domain. A transfer function is a complex function of frequency.
Analyzing a transfer function, especially for evaluating speakers, generally involves
separating the complex quantities into magnitude
Mag(𝑓𝑓) = �Real(𝑓𝑓)2 + Imag(𝑓𝑓)2 [12]
𝐻𝐻(𝑓𝑓) =𝑌𝑌(𝑓𝑓)𝑋𝑋(𝑓𝑓) . [11]
Figure 23: The mapping shows the signal flow in both the time and frequency domain. At any point in the signal chain, translation to and from either domain is possible.
36
and phase
Phase(𝑓𝑓) = tan−1 �Imag(𝑓𝑓)Real(𝑓𝑓)� [13]
and expressing them as plots verses frequency.
For easier visualization, the magnitude is expressed on a decibel scale. In this thesis,
the magnitude responses are primarily normalized by the maximum magnitude such
that the maximum value shown on the figures is 0 dB
Mag (𝑓𝑓) = 10 log10 �Mag(𝑓𝑓)
max�Mag(𝑓𝑓)�� [dB]. [14]
Additionally, the phase is expressed in degrees rather than radians
Phase Deg(𝑓𝑓) = Phase(𝑓𝑓) �180𝜋𝜋 � [deg]. [15]
Once the magnitude and phase values were computed, each was plotted verses
frequency for visual examination. The magnitude was plotted against a logarithmic
scaling to more clearly view the primary frequency range of operation. The phase
was plotted against a linear axis to analyze the linearity of the response.
The frequency response measurements for the second array were performed in the
same anechoic chamber discussed previously. The array was suspended on a
wooden frame such that the speakers were facing the ceiling, and absorbent material
was placed over frame’s reflective surfaces. A microphone was placed a sufficient
distance (~42 inches) above the drivers to ensure the recordings captured no near-
field radiation. This was done by ensuring the kr value was greater than 1 at the
highest frequency of interest (kr~30 at 1500 Hz). The microphone was than aligned
with each driver using a plumb bob. Once aligned, the measurements could begin.
The signal chain for the measurement began with the controlling device and
software, which was again a laptop computer with MATLAB. To output the signal
37
to the speaker, the controlling device communicated with the speakers through a
MOTU UltraLite mk4 input and output audio interface. This interface routed all 21
outputs to a MOTU 24-channel output device. The signals were then sent from this
device through two Dayton Audio 12-channel amplifiers. After amplification, the
signals were sent to the speakers. For recording, a PCB free-field, ½” measurement
microphone was used. This microphone required conditioning from a PCB signal
conditioner, which was connected between the microphone and input device. From
the conditioner, the signal was routed into the MOTU i/o interface and returned to
the system controller with the recorded data. A diagram of the system signal flow is
shown in Fig. 24.
Figure 24: The diagram shows the signal chain used throughout this research for performing frequency response measurements. The left side of the diagram shows the output signal chain while the right side shows the input signal chain.
https://www.parts-express.com/ https://motu.com/en-us/ https://www.pcb.com/
38
This measurement system was used to obtain the frequency responses for all the
speakers in the second array and following arrays. Figure 25 shows this system set
up in the anechoic chamber for the second array iteration. The MATLAB coding
used for these measurements is shown in Appendix D and is an updated and refined
version of coding developed by Miller [18].
3.2.2 Frequency Response Measurement Results
The resulting frequency responses, separated as magnitude and phase, of the drivers
from array two are shown in Figs. 26 through 29. The twelve exterior, Dayton,
drivers are shown first, and the nine interior, Tang Band, drivers shown after. The
magnitude responses include vertical, red lines to indicate the frequency range of
most interest. When analyzing the magnitude and phase responses, the magnitude
responses shown in Figs. 26 and 27 were expected to be relatively flat in the bounded
region as indicated by the specified frequency responses shown in Figs. 17 and 18.
The phase responses in Figs. 28 and 29 were expected to be linear.
Figure 25: In the image, the array is shown mounted on a wooden stand. The measurement microphone is shown towards the top of the image. An extension was added to the microphone stand to ensure the microphone was out of the near-field sound radiation from the speakers. (Miller 2018)
39
Figure 27: Frequency responses (magnitude) for the Tang Band, or exterior, drivers. The frequency range of most importance is between the vertical red lines.
Figure 26: Frequency responses (magnitude) for the Dayton, or exterior, drivers. The frequency range of most importance is between the vertical red lines.
40
Figure 29: Frequency responses (phase) for the Tang Band drivers. Responses were again expected to be linear and tightly grouped.
Figure 28: Frequency responses (phase) for the Dayton drivers. Responses were expected to be linear and tightly grouped.
41
The response data for both driver sets differed from the ideal cases provided in the
specification sheets. The Dayton drivers performed relatively similarly to the
specified response. The main exception was an artifact found in most of the drivers
between 400 and 500 Hz which contained an approximate 10 dB variation. Even so,
the variability was controllable by means of equalization.
The Tang Band speakers, however, performed significantly worse than anticipated.
As a group, these drivers performed erratically with drastically different responses
up to around 700 Hz, and many drivers displayed nearly 20 dB variations over very
short frequency ranges. The differences in responses between drivers was
unexpected and discouraging. While the application of equalization filters would
correct some of these variations, correcting such severe response variability was
impossible with equalization alone.
When analyzing the responses of the drivers, an interesting, non-performance-based
observation was made. Speakers in symmetric positions about the array appeared to
have many similar response characteristics. Figures 30 and 31 show the magnitude
responses for the symmetric driver position groupings. The plots are scaled from
100 to 5000 Hz for better visualization.
Figure 30: Both plots show different magnitude response groupings for symmetric interior driver locations. Both sets of responses share many similarities, particularly above 700 Hz.
42
Analyzing these groupings revealed that the geometric positioning of each driver
within the array carried its own spatial transfer function. Spatial filtering effects due
to geometry would be more prevalent at higher frequencies because of the relative
size of the wavelengths compared to the array dimensions. Interestingly, the
groupings appeared most prevalent among the interior drivers above 700 Hz. The
wavelength of sound at 700 Hz is 0.5 m, which was also the length of the center
posts where these drivers were mounted. From these observations, a general
hypothesis was formed attributing the spatial filtering to radiation from the back
sides of the speakers. If true, this would imply that the lack of grouping at lower
frequencies, and subsequent erratic response behavior was due to the absence of
closed-box baffles. Based on this hypothesis, the possible negative effects of back
radiation on the frequency response of the speakers was more thoroughly examined.
While the speakers were assumed to behave as monopoles, or point sources,
speakers are more accurately represented acoustically as dipole sources. With no
closed-box baffles on the drivers, there was nothing containing the drivers’ back
radiation. A significant portion of back-radiated sound could reach the front of the
array if reflected off a hard surface behind the array. However, when measured in
an anechoic chamber, these reflections are ideally mitigated entirely. Still, back
radiation could remain a problem if the sound diffracts around the array walls or the
anechoic chamber is not entirely anechoic [2]. The diffraction would be particularly
Figure 31: Both plots show different magnitude response groupings for symmetric exterior driver locations. Both sets of responses share many similarities throughout the entire frequency range.
43
problematic at lower frequencies. The diagram in Fig. 32 shows a side profile of the
array and helps visualize the possible propagation paths of back-radiated sound.
This issue may have been more prevalent for the interior drivers because the front
and back-radiation paths were less separated than those of the exterior drivers.
Assuming that a given speaker may be modeled as a monopole is best suited for a
driver placed in an infinite baffle, implying the front and back sides of the drivers
are completely separated. Because of the openings in the array frame, the speakers
were only partially baffled. As Figs. 20 and 21 showed, the exterior drivers had
significantly more baffling material than the interior drivers. The decreased baffling
material may have resulted in increased back-radiation interference for the interior
drivers. This notion was supported by the significantly worse interior driver
magnitude response results. These observations served as the driving rationale for
adding closed-box baffles to future designs.
Figure 32: The diagram shows the possible ways back-radiated sound could reach the front of the array. If back-radiated sound reaches the measurement microphones, the frequency response data would likely be corrupted.
Sound can diffract, or bend, around
the array frame to the front side
44
3.2.3 Noise Cancelling Measurement Results
After the response measurements were obtained, the second array iteration was used
to attempt noise cancellation measurements similar to those performed using the
first array. The drivers were equalized to have as flat and consistent a response as
possible, but significant error was anticipated due to the poor driver responses.
Additionally, the challenges associated with the testing facilities discussed in section
2.3.2 were still present. Because of these issues, expectations for the quality of these
measurements were questionable. However, the noise cancelling measurements
were carried out for the sake of completeness for this array iteration. An image of
the array set up for cancellation measurements is shown in Fig. 33
Unfortunately, the ANC measurements using the second array iteration produced
results which again failed to validate Miller’s numerical solutions. While many
previous challenges were addressed successfully, some new and some old problems
plagued the noise cancelling results again.
Figure 33: In the image, the array is set up facing into the reverberant chamber which again served as the receiving room. A measurement microphone is shown a short distance in front of the array. The anechoic chamber, which again served as the source room, is shown through the window with a primary source set up for the measurements. (Miller 2018)
45
The first problem was unexpected and unique to the second array. When the array
was excited with a broad band signal, a tonal noise (~500 Hz) was heard emitting
from the array. The tone was intermittent and was not caused by any of the signal
filtering being applied. Instead, after examining the structure closely, the tone was
discovered to be radiating from the array frame itself. This was discovered by
holding the array frame to constrain its movement and observing the disappearance
of the tone. The vibration of the speakers was coupling directly to the array structure
and was causing a mechanical vibration at the structure’s natural resonance. Having
this tonal noise present during the measurements was similar to the harmonic content
added due to distortion in the first array iteration measurements. Although some
noise may have been cancelled, the generation of additional tones made the recorded
data challenging to interpret. The different material selection and decrease in array
frame thickness from ¾ inch to ½ inch were determined to be the primary causes of
the structural resonance observed. This mechanical resonance dilemma was
extremely problematic, despite the previously discussed benefits of decreasing the
frame thickness. Ultimately, the negative consequences of reducing the thickness
proved more impactful than the desired gain, so the structure required further
redesign in the third iteration.
The second problem was familiar and arose when attempting to control all the
speakers, including the source speaker, in real time using the controller. Despite the
reduction in number of array drivers from 72 to 21, the control system continued to
struggle performing the measurements without latency issues. This resulted in
several measurements being corrupted by loud, impulse-like pops from the speakers.
These pops occurred when the control system lagged and required some amount of
buffering time. The lagging could have resulted from several different components
of the control system behaving slowly. The different problematic components
proposed were the computer sound card, connection method to the audio interface,
use of MATLAB as the controlling application, or some combination of the three.
While this problem did not cause the poor ANC results, the lagging required that
measurements be ran several times to obtain uncorrupted data and resulted in an
46
inefficient measurement session.
3.2.4 Result Summary
The problems observed from the measurements using the second array iteration
resulted in data which was inadequate and challenging to interpret. To improve the
array design, the poor interior driver responses, tonal radiation due to structural
resonances, and control system latency issues all needed to be addressed before
quality noise cancelling measurements could be obtained. Additionally, a more
acoustically appropriate and accessible lab space was needed for the cancellation
measurements.
47
Chapter 4: Array Iteration 3 To fully address the concerns associated with the second array iteration, the third
array required significant design revisions. This array iteration focused on
improving the acoustical and mechanical designs of the system. The specific
improvements included eliminating the array frame structural resonance and
improving the frequency responses of the speakers in the array. Both objectives were
completed successfully and are discussed in detail in the rest of this chapter.
4.1 Mechanical Design
4.1.1 Array Frame
The first step involved in redesigning the array was to adjust the array’s structural
design. The second array, which experienced the structural resonance issue, was
constructed from ½-inch MDF. Continuing to use MDF as the material was desirable
because of its machinability, so the options for reducing the resonance did not
include changing the construction material. The two options considered for
mitigating the structural resonance were to either add ribbing to strengthen the frame
or to machine another frame at an increased thickness. The cost in time of labor
associated with adding ribbing was deemed more detrimental than the benefits of
using a thinner frame, so a new, thicker frame was machined. The thickness was
increased from ½-inch to 1-inch. A dimensioned drawing of the frame and an image
comparing the array frame thicknesses from each iteration are shown in Figs. 34 and
35.
48
Figure 34: The third array frame designed is shown fully dimensioned using AutoCAD. The dimensions are again in inches.
Figure 35: The arrays are placed in chronological order from left to right. The leftmost frame is iteration 1 (plywood), the center frame is iteration 2 (MDF), and the rightmost frame is iteration 3 (MDF).
49
The resulting array frame was significantly more massive and rigid than the second
iteration’s frame. While a thorough structural vibration analysis was not performed
to determine the new frame’s resonance characteristics, the thicker design was
deemed sufficient for mitigating the previous structural resonance issue.
4.1.2 Closed-Box Baffles
The next step in redesigning the array was to add enclosures to the back side of the
array drivers. As discussed previously, the baffling provided by the array frame itself
was poor and was determined to contribute significantly to the corruption of the
frequency response results. To remedy this, the best determined solution was to add
enclosures, or back volumes, to the back side of the drivers to create a closed-box
baffle. A closed-box baffle completely isolates the front and back sides of the
speaker and approximates an infinite baffle well [2]. When compared to just the
array frame, the closed-box baffle was a far superior design.
For the initial addition of enclosures to the array, manufacturing flexibility was
considered more important than the optimizing the acoustical design. Instead of
designing a fine-tuned enclosure for the speakers, a more generic design which
could be easily purchased, added, and removed from the array frame was chosen.
To meet these requirements, 3-inch and 2-inch diameter PVC pipe endcaps were
purchased and attached to the back of the array. The volume of each enclosure was
350 and 125 mL, respectively. To ensure total separation from the front and back
sides of the drivers, the enclosures needed to form an air-tight seal with the surface
of the array frame. To do this, adhesive putty was used to attach the enclosures to
the array surface. The speaker leads were then run through the enclosures for the
internal speakers and under the enclosures for the exterior speakers. An image of
the construction is shown in Fig. 36.
50
The wiring for the speakers was designed to be easily removable for setting up and
tearing down the array when performing measurements. A diagram of the wiring
method used is shown in Fig. 37. In the figure, a single, split cable travels from
the amplifier to each speaker. Alligator clip jumper cables were used to attach
the signal cable to the speaker leads. The leads for the interior, Tang Band,
drivers were small wires which were run through small holes in the PVC
enclosures. The leads for the exterior, Dayton, drivers were only small solder
tabs located close to the speakers. Rather than solder wire leads onto the tabs
and run them through the PVC, the alligator clips were run underneath the
exterior enclosures and connected directly to the tabs. All enclosures were
checked to ensure no significant air leakage occurred due to the wiring. While
not robust or neat enough for a final product, the wiring structure provided necessary
versatility for the frequent adjustments made during testing.
Figure 36: The left image shows an interior driver enclosure with the leads exiting through the PVC. The right image shows an exterior driver. The leads for these eventually ran underneath the enclosures.
51
After all the enclosures were attached, the array was painted to improve its visual
aesthetic. Images of the painted assembly are shown in Fig. 38 displaying the back
of the array with all of the speaker enclosures and the front of the array with the
speaker diaphragms.
Figure 37: Output signal chain and wiring to the speakers.
Figure 38: The left image shows the painted back side of the array. The right image shows the front side of the painted array. One visible downside of the wiring method used is its disarray.
https://www.123rf.com/stock-photo/alligator_clips.html?sti=mlrder87we80b0hpre|
52
4.2 Acoustic Design
4.2.1 Closed-Box Baffle Modeling
After the addition of the closed-box baffles, the array was ready to undergo
frequency response performance testing. To estimate the driver responses with the
enclosures, a theoretical model was created of a speaker in an enclosure using an
analogous circuit simulation in LTspice. The simulated frequency response
approximations for both driver types assume ideal, linear component performance.
The circuit specifically for the Tang Band drivers is shown in Fig. 39. While the
component values change between circuits, the circuit structure was identical for
both drivers.
In the circuit model, most values were obtained directly from the specification sheets
of each driver. The mechanical resistance, R2, and the acoustical compliance, C2,
were the only basic components which required additional computations
𝜋𝜋𝑚𝑚 = 𝜋𝜋2 =2𝜋𝜋𝑓𝑓𝑛𝑛𝑀𝑀𝑚𝑚𝑛𝑛
𝑄𝑄𝑚𝑚𝑛𝑛 [
N − sm ] [16]
𝐶𝐶𝑎𝑎𝑎𝑎𝑛𝑛 = 𝐶𝐶2 =𝑉𝑉𝜌𝜌𝑐𝑐2 �
m5
N�. [17]
Figure 39: The LTspice circuit model approximates a speaker in a closed-box baffle. Section A of the circuit represents the electrical domain, section B of the circuit represents the mechanical domain, and section C of the circuit represents the acoustical domain.
A B
C
53
The gyrator, transformer, radiation impedance, and SPL components were slightly
more complicated structures and were designed by Thompson [26].
The Thiele Small parameters for both drivers were obtained from the specification
sheets shown in Appendix A. Values of the parameters used in the LTspice models
for each driver are shown and compared in TBL. 2. Additionally, the air density and
speed of sound values used in the model were 1.23 kg/m3 and 343 m/s, respectively.
Using these Thiele Small parameters in the LTSpice model shown in Fig. 39, the
theoretical frequency responses were obtained for each driver. These are shown in
Figs. 40 and 41.
Table 2: The Tang Band and Dayton driver Thiele Small parameters used in the theoretical models are compared.
54
These simulations provided a target frequency response to aim for when measuring
the actual driver frequency responses. While these ideal responses would not be
replicated exactly, the measured responses were hoped to somewhat resemble the
simulations.
Figure 41: The figure shows Tang Band driver’s theoretical magnitude response.
Figure 40: The figure shows the Dayton driver’s theoretical magnitude response. The input amplitude was set such that the maximum magnitude value was close to 0 dB. The frequency range was limited to 80-10,000 Hz.
55
4.2.2 Frequency Response Measurement Results
The driver frequency responses were measured using the same methods discussed
in section 3.2.1. The results were expected to show smoother, more unified
responses for both driver sets, especially in the low frequency region. The magnitude
responses for the exterior drivers are shown in Fig. 42. Figure 43 then shows the
interior driver responses. The figures are shown together for comparison. As done
previously, the magnitude responses were normalized to a maximum of 0 dB and
vertical red lines highlight the frequency range of most interest. The figures showed
that while the exterior driver responses improved as expected, the interior driver
responses remained poor with the same large variations in magnitude as measured
previously. Figures 44 and 45 show the phase responses for both driver sets. Then,
Figs. 46 and 47 show a comparison of magnitude responses with enclosures and
without enclosures.
56
Figure 42: Frequency responses (magnitude) for the Dayton drivers. The responses showed significant improvement with a tight grouping and less than 5 dB of variation from each other.
Figure 43: Frequency responses (magnitude) for the Tang Band drivers. The responses showed no improvement with poor grouping and large variations.
57
Figure 44: Frequency responses (phase) for the Dayton drivers. The responses are tightly grouped.
Figure 45: Frequency responses (phase) for the Tang Band drivers. The responses are not tightly grouped.
58
Figure 46: Frequency response comparison (magnitude) for the Dayton drivers with and without closed-box baffles, or back volumes.
Figure 47: Frequency response comparison (magnitude) for the Tang Band drivers with and without closed-box baffles, or back volumes.
59
When analyzing the results of the magnitude responses, some clear improvements
were observed. The artifact around 450 Hz in the exterior driver responses which
was present in nearly all the previous responses was smoothed out completely.
Additionally, the spatial filtering effect shown in Figs. 30 and 31, which showed
groupings of the responses for drivers at symmetric locations, did not occur after the
enclosures were added This confirmed the prior hypothesis regarding the closed-
box baffles’ effect on spatial filtering. Both of these observations showed
conclusively that the addition of the closed-box baffles improved the exterior driver
responses. Unfortunately, when analyzing the results for the interior drivers, little to
no improvements were noticed. The phase responses revealed similar trends. While
both response sets remained linear, the grouping uniformity was noticeably worse
for the Tang Band drivers.
Recall that the goal of improving the frequency responses was to smooth and unify
the magnitudes over the frequency range of interest to maximize the effectiveness
and efficiency of the equalization filters. With this in mind, the exterior drivers
appeared to be smooth enough to successfully apply equalization filters. Conversely,
the interior driver responses needed to be improved significantly before effective
equalization was possible.
Luckily, the adjustment needed to improve the interior driver results was simple.
When constructing the array, the interior drivers were press-fit into the routed holes
and glued in place. Upon investigation, it was determined that the glue was not
providing an airtight seal between the fronts and backs of the drivers, meaning air
was leaking around the edges. This rendered the closed-box baffles ineffective as
there was no separation between the front and back sound radiation. By adding some
adhesive putty, airtight seals were formed around the driver circumference, and the
responses were remeasured. The image in Fig. 48 shows the array with the added
putty. The frequency responses were then remeasured. The magnitude and phase
responses are shown in Figs. 49 and 50, respectively. Additionally, a comparison of
the new magnitude responses to the previous magnitude responses is shown in Fig.
51.
60
Figure 48: The image on the left shows the entire array where the interior drivers have putty seals added. The right image shows a close-up of one driver with the putty added. While the putty would not be viable as a long-term solution, the addition provided a quality temporary resolution.
Figure 49: New frequency responses (magnitude) for the Tang Band drivers. The new magnitude responses are significantly better than previously measured. While they are not as smooth and tightly grouped as the Dayton responses shown in Fig. 42, the Tang Band responses are much improved.
61
Figure 51: Frequency response comparison (magnitude) for the Tang Band drivers with and without putty and closed-box baffles. The magnitude responses were improved significantly.
Figure 50: Frequency responses (phase) for the Tang Band drivers. The responses are grouped significantly tighter than previously shown in Fig. 45.
62
These results showed that the addition of the putty to the drivers significantly
improved the frequency responses. The magnitude responses were grouped much
more tightly, and despite some regions of variation, were much smoother than
previously measured. Maximum variations decreased from upwards of 25 dB in the
previously measured responses to around 10 dB in the new responses. Any
variations in the new responses occurred more gradually than before as well.
Additionally, the phase responses were grouped more tightly than previously shown.
Altogether, these results boasted significant improvements in comparison to
previously measured results. For a final point of comparison, both drivers’ averaged
magnitude responses were compared to their ideal responses obtained from the
LTspice simulations shown previously in Figs. 40 and 41. The results are shown
in Figs. 52 and 53.
For the Dayton drivers, the averaged measured response matched the simulated
response fairly well. Particularly, the low frequency region from 20 to 600 Hz
matched very well. The measured responses had a moderate recession in the mid
frequency region but met back up with the ideal curve in the high frequency region.
Figure 52: Averaged magnitude response for the Dayton drivers compared to LTspice simulated magnitude response. The ideal and measured responses match quite well.
63
For the Tang Band drivers, the averaged measured response matched the simulated
curve decently, but not as well as the Dayton speakers. Again, the low frequency
region appeared to be the area of closest coincidence.
By normalizing the averaged measured response to a peak of 0 dB, the variation in
the measured responses was deemed responsible for some discrepancy between the
measured and simulated results. Recognizing this, the simulated response was
adjusted to a best fit location for the measured responses. This showed that the
measured responses genuinely matched the simulated responses quite well.
This conclusion served to further validate that the addition of the putty to the drivers
successfully improved the interior driver frequency responses. Further, the addition
of the closed-box baffles to the array conclusively improved both driver responses
significantly. Upon validating the array design improvements, all drivers were able
to undergo equalization (EQ) filter testing.
Figure 53: Averaged magnitude response for the Tang Band drivers compared to LTspice simulated magnitude response. The ideal and measured responses match relatively well.
64
4.2.3 Equalization Filters
The EQ filter writing process used was developed by Miller and is discussed
more thoroughly in his thesis. In short, the equalization filters are a combination
of the inverted driver transfer functions and a bandpass filter. The inverted
transfer function serves to smooth the magnitude response, while the bandpass
filter limits the applicable gain at the low and high frequencies. When one of
these unique EQ filters is applied to its corresponding transfer function, an ideal,
equalized frequency response is obtained. Figures 54 through 56 show this
process as a series of plots.
Figure 54: The plot to the left shows an arbitrary driver’s magnitude response measured using the methods discussed previously. The second plot shows that same response along with the inversion of itself.
65
The ideal, equalized response above was the target for all drivers in the array. As
explained previously, the goal of the equalization process was to generate as similar
responses as possible among all drivers in the array.
Figure 55: The left plot shows the bandpass filter magnitude response used to tame the extreme gains of the inverted filter at low and high frequencies. The right plot shows the bandpass filter combined with the inverted transfer function to form the total EQ filter for that specific driver.
Figure 56: The left plot shows the total EQ filter and original magnitude response of the driver. Multiplying those two responses together yields the ideal, equalized response shown in the right plot.
66
To test the equalization filters, the frequency responses were measured as done
previously. The only change in the process was that the measurement signal used,
an exponential sine sweep, was filtered using each driver’s unique EQ filter. The
equalized measurement signals were unique for each driver because the EQ filters
included each driver’s unique inverse transfer function. To filter the measurement
signal, the sine-sweep and equalization filter were multiplied point-by-point in the
frequency domain
𝑥𝑥2(𝑡𝑡) = 𝑖𝑖𝑓𝑓𝑓𝑓𝑡𝑡�𝑓𝑓𝑓𝑓𝑡𝑡�𝑥𝑥1(𝑡𝑡)�EQ(𝑓𝑓)� [18]
where x1 is the sine sweep, x2 is the filtered sine sweep, and EQ is the equalization
filter. Figure 57 shows the time domain input signal used for the original
frequency response measurement and one of the new, filtered time-domain input
signals used to test the EQ filters.
Figure 57: The plot compares the original input signal to the filtered input signal. The filtered sweep has an amplitude change somewhat similar to the filter magnitude response.
67
One interesting observation here was that because the input signal was an
exponential sine sweep, the amplitude shaping in the time domain somewhat
corresponds visually to the magnitude response. Notice that the beginning of the
time signal, which contains low frequency content, was suppressed significantly
more than the mid frequency region. This corresponds to the suppression of low
frequency content caused by the bandpass filter portion of the EQ filter. Other
amplitude shaping in the mid frequency range corresponds to the unique inverse
transfer function used in the equalization filter.
The equalization filters were then tested by remeasuring the frequency responses of
each driver using the new, uniquely filtered input signals. The filtered magnitude
responses for both driver sets are shown in Figs. 58 and 59 with bars marking +/-
2.5 dB.
Figure 58: Equalized magnitude responses for the Dayton drivers. The green dashed lines show that the responses vary by less than 5 dB. Note that the responses are now normalized by 1 as opposed to the max value as done previously. This helps to better visualize the quality of the EQ filters.
68
When analyzing the equalized magnitude responses, the exterior driver responses
appeared to be flatter and more tightly grouped than the interior responses. Still,
both sets of equalized responses were relatively tightly grouped with less than 10dB
of amplitude variation among the responses, and both would be acceptable to use
for baseline active noise cancelling measurements. However, for optimal results, the
equalized responses would ideally be even smoother with no more than 5 dB of
gradual variation.
One interesting observation was that a few very flat curves were embedded in the
groupings which closely resembled the ideal equalized response shown in Fig. 56.
This occurred as a result of the measurement methods used. When testing the EQ
filters, the unfiltered responses were measured first for all drivers. The measurement
microphone location was aligned on axis with each driver using a plumb bob, and
the locale moved with each successive measurement. The spatial orientation of the
microphone with respect to the measured driver influenced some characteristics of
each driver’s unique frequency response. Meaning that some of the variations in the
magnitude responses were due to the relative microphone location and not just the
Figure 59: Equalized magnitude responses for the Tang Band drivers. The green dashed lines show that the responses nearly vary by less than 5 dB.
69
drivers’ acoustic behavior. Later, when the equalized frequency responses were
measured for each driver, the relative microphone location was not identical to its
first location. The relative spatial differences between the two different microphone
locations resulted in equalized responses with some variations. Theoretically, if the
microphone locations had been identical for both measurements, the equalized
responses would be completely flat.
To test this, both the non-equalized and equalized frequency responses for a unique
driver were measured in succession without disturbing the microphone location.
Using this method, the equalized response was nearly identical to the ideal equalized
response. Figure 60 shows a comparison of one of these measured responses to the
ideal equalized response.
When the spatial orientation of the microphone relative to the measured driver did
not change, the measured equalized responses matched the ideal equalized response
very well. Unfortunately, any application using the ANC system would require the
array to be removed from the anechoic chamber. Meaning that any spatial filtering
Figure 60: The plot shows an equalized magnitude response when the measurement environment is untouched between the initial frequency response and the EQ’d frequency response measurement. The equalized response matches the ideal EQ’d response very well.
70
effects caused by the measurement setup used to obtain the EQ filters would be
present in the equalized responses when used in any other location. This implied
that the outstanding equalized response shown above in Fig. 60 would likely never
be achievable in any other measurement environment. For example, if the EQ filters
were applied to the drivers while the array was mounted to an office window for
ANC purposes, the spatial filtering caused by the frequency response measurement
environment would result in imperfect equalization. Despite this disappointing
realization, the majority of each driver’s response characteristics were genuinely due
to its acoustic performance. So, while the drivers may never be equalized perfectly,
the responses will still be significantly flatter than without the equalization filters at
all.
Although perfect equalization was determined to be impossible, improvements
could be made to the EQ filters to mitigate the spatial filtering problem discussed
above. The artifacts associated with spatial filtering often appear as sharp dips or
peaks in a frequency response. Because the EQ filters use the exact inversion of the
frequency response, these peaks and dips also appear in the EQ filter. If the artifacts
are genuinely caused by the spatial filtering, applying the EQ filter in a different
environment will incorrectly equalize the response. For example, if a spatial filtering
artifact was a sharp 10 dB dip, the EQ filter would contain a sharp, 10 dB peak at
the same frequency. If the EQ filter was applied in a different environment, the 10
dB dip may no longer be present, but a 10 dB boost would still be applied at that
frequency, despite having been ‘equalized’.
One way to avoid applying dramatic incorrect gains would be to remove some of
the fine detail in the equalization filters. Smoothing the EQ filter maintains the
general frequency response shape while dampening the sharp peaks and dips. This
could be done easily by adding a moving average filter to the EQ filter. This method
allows for the retention of any amount of detail in the frequency response, as the
size of the moving average filter determines its resolution. Figure 61 shows an
example of this applied to a total EQ filter magnitude response.
71
Using a moving average filter forces the magnitude response to be more generic,
which may more accurately represent the acoustic response of the speakers. Ideally,
the smoothing would only remove added effects due to the measurement
environment and retain all effects due to driver performance. Unfortunately, the
smoothing process cannot distinguish between spatial and acoustic artifacts in the
frequency responses, so using the additional smoothing filter carries some risk of
removing genuine speaker response characteristics. Because of this, using a moving
average filter is recommended for future work but should be used with caution. If
used well, the moving average filter can be a useful tool for improving the accuracy
of the equalization filters.
Figure 61: The plot shows the same filter frequency response shown in Fig. 55 with smoothing and no smoothing. The smoothing was generated using a 30-point moving average filter.
72
Chapter 5: Measurement Facility To perform quality ANC measurements, the measurement facility used needed
several improvements. The first task for improvement was to acquire a new
measurement facility. The inaccessibility of the prior facility made consistent and
efficient testing impossible. Additionally, the constraint of using a reverberant
chamber as either the receiving or source room resulted in data analysis
complications. This chapter covers the development of a new lab space dedicated to
the experimentation for this research project.
5.1 Selection and Construction The new lab space allotted to the TDL, referred to as Room 22, was a significantly
larger room than the coupled anechoic and reverberant chambers. The room was still
somewhat reverberant because of its concrete floor and walls, but its large size and
presence of some absorbent material resulted in a significantly less reverberant
space than used previously. The reverberation time for the new lab space was
estimated to be 1-3 seconds compared to the reverberant chamber’s 4-6 seconds.
Unfortunately, the lab space did not contain any isolated rooms or spaces which
approached a free-field environment like the anechoic chamber used previously.
This type of space was deemed a necessity for performing quality acoustic
measurements, so a semi-anechoic, noise-isolation measurement structure was
purchased from Whisper Room Inc. The room purchased was 8-by-10-by-8 feet and
included 1-inch thick, MDF walls for noise isolation, rubber floor padding for floor
vibration isolation, a removable transmission window for performing the ANC
measurements, and 2-inch thick acoustic foam paneling for reflection reduction.
Additionally, the room included lockable wheels for easy movement, a ventilation
system to maintain air flow, and pluggable ports for cable introduction from outside
the room. The room specification sheet, images of the specific features, and a
73
walkthrough of the room assembly are given in Appendix B. The room was
constructed in-house with the help of some fellow PSU students over the course of
around two months. An image of the fully constructed Whisper Room from the
exterior is shown in Fig. 62. Upon the completion of construction, the Whisper
Room isolation capabilities were analyzed.
5.2 Transmission Loss Overview The primary requirement for the testing facility was that it perform quality sound
isolation, or that it had high transmission loss. When performing noise cancelling
measurements, the only significant sound transmission present should be through
the open window. Acoustically, measurable noise reduction is limited by the quality
of the noise source isolation from the measurement microphones. For example, if a
noise cancelling system was installed in a window of a wall, and the wall only
provided 5 dB of transmission loss, the maximum measurable noise cancellation
would only be 5 dB. In short, active noise attenuation through a window will only
appear as effective as the passive attenuation of the measurement environment. Even
Figure 62: Fully constructed sound isolation chamber. The open door shows the foam paneling used to cover the interior of the room. The stock window for the Whisper Room products was conveniently similar in size to the array. The total construction time was around two months.
74
if the ANC system was providing significant cancellation, the noise passing through
the wall would limit the measurable reduction. The example illustrated in Fig. 63
clarifies this concept.
The figure shows an example where a source is producing 80 dB of noise. The sound
coming through the window is reduced by 20 dB due to the ANC system. However,
the walls provide only 5 dB of reduction. The sound level measured at the
microphone would be much higher than the 60 dB expected from the ANC
performance. The resulting measurement would not accurately capture the 20 dB
reduction of the ANC system and would lead to a gross misrepresentation of the
ANC performance.
Because of this, the new testing facility needed to provide more sound isolation than
expected active noise reduction. Based on Miller’s work in conjunction with other
research discussed previously, the expectations for noise reduction ranged from 10
to 20 dB over the frequency range of 1500 to 300 Hz, respectively. The minimum
buffer deemed necessary to ensure the accuracy of these measurements was 5 dB.
-5 dB
80 dB
-5 dB
-20 dB 60 dB
75 dB
75 dB
Figure 63: The figure above supports the below example. In the figure, the noise source is located to the left. A wall with a secondary source array is shown in the center with a measurement microphone shown to the right. The arrows represent the noise propagation paths.
75
This buffer meant that the measurement room needed to provide at least 5 dB more
isolation than active noise reduction for the ANC data to be considered accurate.
Specifically, this meant that at 300 Hz, the passive reduction needed to be at least
25 dB to accurately measure the expected 20 dB of active noise reduction. At 1500
Hz the passive reduction would need to be at least 15 dB. This demand contradicted
the fact that lower frequencies are affected less by passive attenuators than high
frequencies. Still, the Whisper Room proved capable of meeting most of the
conservative transmission loss demands.
Whisper Room’s website provided a tool for estimating the amount of reduction a
single wall would provide for a given input noise level. The program approximated
the passive reduction levels at octave bands ranging from 125-4000 Hz. The
transmission loss results for a wall exposed to a 75 dB noise source are shown in
Fig. 64. Note when observing the diagram that the room purchased for this project
utilized standard walls. These results were used as a point of comparison for the
measured transmission loss results the Whisper Room made with six of these walls
and are discussed in the section 5.5.
5.3 Transmission Loss Measurement Method The transmission loss measurements performed mostly adhered to the ISO 140-4
standard for field measurements of airborne sound insulation between rooms [21].
While this particular ISO standard targets adjacent rooms separated by a wall, the
standard was extrapolated to fit the measurement scenario of a room inside a larger
room.
The first measurement design decision was to determine which room would be the
source room and which room would be the receiving room. Generally, the source
and receiving room choices are up to the user’s discretion. The principle of
Figure 64: The figure shows the estimated amount of sound isolation at octave bands. The sound isolation in the frequency region of interest appears to be steadily around 25 dB.
https://whisperroom.com/noise-reduction/
76
reciprocity in acoustics dictates that the transmission loss provided by the barrier
will be the same regardless of which room is source and receiving. While this was
true, an analysis of the noise floors for both rooms revealed the interior room was
better suited for the receiving room.
To capture the noise floors, one-third octave band measurements were taken using
the sound level meter shown in Fig. 65. The sound level meter used was a Brüel &
Kjær Type 2250 with a 1/2-inch free-field microphone.
Measurements were taken at three different locations in each room for thirty seconds
and then averaged. The results showed that the housing room, Room 22, had a much
higher measured noise floor than the sound isolation room, Whisper Room. Figures
66 and 67 show the unweighted, one-third octave filtered noise floors for Room 22
and the Whisper Room, respectively. Note that all sound pressure level (SPL)
measurements taken were corrected to account for the self-generated noise of the
combined microphone and electrical systems of the sound level meter. This is
discussed further in Appendix C.
Figure 65: The image on the left shows the sound level meter mounted on a stand as used for measuring the noise floor in Room 22. The image on the right shows the front panel of the sound level meter.
https://www.bksv.com/en/products/measuring-instruments/sound-level-meter/2250-series/Type-2250-S
77
Figure 66: Z-weighted Room 22 noise floor at 1/3-octave bands. The total, A-weighted sound pressure level is given in the top-right corner of the figure.
Figure 67: Z-weighted Whisper Room noise floor at 1/3-octave bands. The total, A-weighted sound pressure level is given in the top-right corner of the figure. Note the increased infrasonic octave bands on the left end of the figure.
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
SPL
(dB)
1/3 Octave Frequency Bands (Hz)
𝑳𝑳𝑨𝑨𝒆𝒆𝒆𝒆 = 𝟒𝟒𝟒𝟒.𝟓𝟓 𝒅𝒅𝒅𝒅
-20.00
-10.00
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
SPL
(dB)
1/3 Octave Frequency Bands (Hz)
𝑳𝑳𝑨𝑨𝒆𝒆𝒆𝒆 = 𝟐𝟐𝟐𝟐.𝟖𝟖 𝒅𝒅𝒅𝒅
78
The results revealed that the Whisper Room noise floor was significantly lower than
in Room 22, especially in mid to high frequency regions. At very low frequencies,
specifically below the audible range, the Whisper Room had elevated noise levels
compared to the housing room. This showed that despite the addition of vibration
isolation padding, some amount of coupling was occurring between the isolation
chamber and the floor of the housing room. Some of this may have been caused by
the room’s location relative to a nearby busy street. Regardless of the cause, this
frequency regions location was well outside the region of interest for ANC, so the
presence of elevated infrasonic signals was deemed negligible.
The significant differences in noise floor levels was the determining factor for
choosing which room would serve each role in the measurements. The ISO standard
suggests for quality measurements, all measured signals be at least 10 dB above the
noise floor at relevant one-third octave frequency bands [21]. For this measurement,
this implied that the receiving room noise floor needed to be at least 10 dB lower
than any detected signal at the respective frequency band. Additionally, as discussed
previously, transmission losses up to nearly 30 dB in the range of interest were
expected based on the Whisper Room estimations. Combining this expectation with
the ISO suggestion revealed that the difference between the noise floor of the
receiving room and the noise generated by the sources needed to be approximately
40 dB. Understanding the principle of reciprocity in conjunction with this
conclusion revealed that the noise sources would require lower driving amplitudes
if the housing room was the source room and the Whisper Room was the receiving
room. Table 3 displays the sound level differences in necessary drive level
depending on the room orientation.
In the table, the left numerical column gives the total A-weighted noise floor for
each room. The next column simply adds the 10 dB buffer suggested by the ISO
standard. The last column then adds 30 dB to each total to account for the
transmission loss provided by the Whisper Room. The values in this last column
represent the SPL of the source generated noise necessary to ensure that the noise
signals were legitimately measurable.
79
After determining source and receiving room designation, the next step in the
measurement design was to determine what noise sources to use and their orientation
in the source room relative to the receiving room. The ISO standard recommends
using omnidirectional sources to ensure a diffuse sound field [21]. The sources used
were two omnidirectional speakers. The first covered lower frequencies using two
subwoofers. The second covered the mid-frequency range and consisted of 12
drivers. Together, the speakers provided a relatively flat response over the desired
frequency range. The components of the output signal chain, including an amplifier
and both speakers, are shown in Figs. 68 and 69, respectively.
Figure 68: The amplifier used was a Crown XLS 2500 and was provided by the SPRAL lab.
Table 3: Sound pressure levels in dB which reveal why the Whisper Room was chosen to be the receiving room.
https://www.crownaudio.com/en/products/xls-2500
80
The ISO standard also proposed placing the sound sources in a position that
minimizes direct sound transmission to the microphone [21]. While using an
omnidirectional source diminishes this effect, the sources were still placed in the
corner of the room to further ensure the generation of a diffuse field. Additionally,
the ISO standard required that the minimum amount of different source locations be
two if the microphone location varied for each measurement. Because of this, a
second corner of the housing room was selected as the second source location.
After settling on source locations, the sound level meter was positioned. When using
two noise source locations, the ISO standard calls for measurements at five different
locations [21]. These measurement locations were to be separated by at least 0.7
meters. The goal of measuring in different locations was to avoid capturing
artificially increased or decreased amplitudes caused by room modes. To determine
the various measurement locations, a single, primary locale was established for
Room 22 and the Whisper Room. From this primary location, four secondary
measurement points were established on a one-meter radius sphere and at a 90-
degree azimuth angle relative to each other. With this design, each measurement
Figure 69: The left image is of the omnidirectional subwoofer, and the right image is of the omnidirectional mid-range speaker. Fundamental acoustics serves to remind that lower frequency sources radiate with a more omnidirectional directivity. Hence, subwoofer requires only two unique drivers while the mid-range source contains twelve to achieve omnidirectional radiation. These sources were generously provided by the SPRAL acoustics lab [6].
81
location was guaranteed to be at least 0.7 meters away from all other measurement
locations. To meet the ISO standard, recordings were to be taken at these five
different microphone locations for both rooms and both sound source locations. This
meant 20 total measurements were necessary to obtain an accurate assessment of
the transmission loss provided by the Whisper Room. A diagram of the experimental
setup is shown in Fig. 70.
In the figure, the source locations are shown on the left, while the measurement
locations are shown on the right. The primary locations are shown as sound level
meters while the secondary locations are shown as black dots. The distances
between the source and receiving locations are shown on the figure as well. The
distances were purposefully set to be relatively similar to avoid differences in losses
due to spherical spreading.
Figure 70: The figure represents a top-down view of the lab space and experimental setup for the transmission loss measurements. Note that the secondary measurement locations were oriented at differing heights. The figure also shows the output signal chain running from the controller, through the amp, and to the speakers.
82
Upon the completion of the experimental setup, the only remaining task was to
determine the type of noise signal to use. Adhering to the ISO standard required
limiting the variation in adjacent one-third octave bands to 6 dB. White noise was
chosen as the measurement signal because the signal contains equal intensities at all
frequencies. The signal was generated by a controlling laptop using MATLAB.
5.4 Decibel Arithmetic Before discussing the noise measurement results, understanding how the noise
levels are expressed and the arithmetic associated with finding average and
differential sound pressure levels is necessary. For these measurements, the noise
levels were expressed as both unweighted one-third octave band decibel values and
as a total, A-weighted decibel values. Decibels are units used to express power or
power-like quantity ratios on a logarithmic scale. Pressure levels are more
appropriately expressed as decibels because of their large variation in magnitude.
Sound pressure level is the decibel scaled unit used to represent the effective sound
pressure relative to an arbitrary reference pressure [2]
𝑆𝑆𝑆𝑆𝐿𝐿 = 10 log10𝑝𝑝𝑗𝑗𝑚𝑚𝑛𝑛2
𝑝𝑝𝑗𝑗𝑛𝑛𝑑𝑑2 dB. [19]
For air, the reference pressure is 20µPa. Additionally, averaging was crucial to
obtaining accurate noise level results. Performing arithmetic averaging required that
the data from several measurements be addible. Because of the scaling applied to
sound pressure levels, decibel values cannot be added in the same way as normal
integers. To add sound pressure levels, the decibel values must be converted to
power like quantities [23]
𝑝𝑝𝑗𝑗𝑚𝑚𝑛𝑛2 = 𝑝𝑝𝑗𝑗𝑛𝑛𝑑𝑑2 10
𝑆𝑆𝑆𝑆𝑆𝑆10 Pa2. [20]
83
Once the data sets have been converted to the squared pressure values, the arithmetic
mean can be taken normally
𝑝𝑝𝑎𝑎𝑎𝑎𝑎𝑎2 =𝑝𝑝𝑗𝑗𝑚𝑚𝑛𝑛1
2 + 𝑆𝑆𝑗𝑗𝑚𝑚𝑛𝑛22 + 𝑆𝑆𝑗𝑗𝑚𝑚𝑛𝑛3
2 + 𝑆𝑆𝑗𝑗𝑚𝑚𝑛𝑛42 + 𝑆𝑆𝑗𝑗𝑚𝑚𝑛𝑛5
2
5 , [21]
and the average SPL is computed from the averaged squared pressure
𝑆𝑆𝑆𝑆𝐿𝐿𝑎𝑎𝑎𝑎𝑎𝑎 = 10 log10𝑝𝑝𝑎𝑎𝑎𝑎𝑎𝑎2
𝑝𝑝𝑗𝑗𝑛𝑛𝑑𝑑2 . [22]
The above method was used extensively to perform averaging for measured noise
levels. In addition to performing averaging, further computations were needed to
account for the self-noise of the sound level meter. To do this, the self-noise was
subtracted from the averaged, squared pressure values
𝑝𝑝𝑎𝑎𝑎𝑎𝑎𝑎𝑗𝑗𝑎𝑎𝑟𝑟2 = 𝑝𝑝𝑎𝑎𝑎𝑎𝑎𝑎2 − 𝑝𝑝𝑛𝑛𝑛𝑛𝑑𝑑𝑑𝑑−𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛2 . [23]
Again, because of the logarithmic scaling, these computations needed to occur as
power-like quantities. The averaged SPL of the measured noise alone was then
𝑆𝑆𝑆𝑆𝐿𝐿𝑎𝑎𝑎𝑎𝑎𝑎_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 10 log10𝑝𝑝𝑎𝑎𝑎𝑎𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟2
𝑝𝑝𝑗𝑗𝑛𝑛𝑑𝑑2 . [24]
Lastly, for the transmission loss measurements, one additional calculation was
needed to find the sound level reduction. Computing transmission loss is much
simpler than performing averaging because it involves a comparison of measured
sound pressure levels. This means to find the sound reduction, only a subtraction of
averaged SPL values is needed
𝑇𝑇𝐿𝐿 = 𝑆𝑆𝑆𝑆𝐿𝐿𝑊𝑊𝑗𝑗 − 𝑆𝑆𝑆𝑆𝐿𝐿𝑗𝑗22. [25]
As with the SPL data, the transmission loss values were expressed both in one-third
octave bands and as a single, A-weighted values.
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5.5 Transmission Loss Measurement Results The first set of measurements was performed in Room 22. For these measurements,
five, 30 second measurements were taken at different locations and were averaged
to obtain an accurate assessment of the noise outside the Whisper Room. The
measurement signal was 76 dB of white noise. The same measurement process was
then used to measure the noise levels in the Whisper Room. Figures 71 and 72 show
the measured average noise levels in Room 22 and in the Whisper Room,
respectively.
The Room 22 results showed that the level of each band was within 6 dB of adjacent
bands with the exception of the 1250 and 1600 Hz bands. Meaning, that while the
ISO standard was not met perfectly, the output signal was fairly flat across the
frequency spectrum. This one variation of around 10 dB likely occurred because an
omnidirectional tweeter was not included with the noise sources. Despite this, the
generated noise was deemed sufficient for performing the transmission loss
measurements.
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00 𝑳𝑳𝑨𝑨𝒆𝒆𝒆𝒆 = 𝟕𝟕𝟓𝟓.𝟖𝟖 𝒅𝒅𝒅𝒅
Figure 71: Z-weighted Room 22 measured white noise levels at 1/3-octave bands.
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The results from the Whisper Room noise measurements contained some expected
and unexpected results. The increased levels in the infrasonic region were not
surprising given the increased noise floor levels in those same frequency bands. The
increase in the 63 and 80 Hz bands was not expected though and was likely caused
by a structural resonance of the wall panels of the Whisper Room.
After measuring and averaging the noise levels for both rooms, the averaged
transmission loss provided by the Whisper Room was determined. Figure 73 shows
the transmission loss for one-third octave bands computed using equation 25 from
section 5.4. The total A-weighted transmission loss was determined to be about -23
dB.
Figure 72: Z-weighted Whisper Room measured white noise levels at 1/3-octave bands.
-20.00
-10.00
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00 𝑳𝑳𝑨𝑨𝒆𝒆𝒆𝒆 = 𝟓𝟓𝟐𝟐.𝟔𝟔 𝒅𝒅𝒅𝒅
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The transmission loss results revealed the same interesting results found in the
Whisper Room noise levels shown previously. Namely, that the Whisper Room
appeared to enhance infrasonic noise when excited by an external noise source. This
was consistent with the differences in background noise level between the rooms
shown previously. Regardless, for this project the boost in infrasound will not
provide significant hindrance to obtaining quality ANC results. Still, awareness of
this abnormality is useful information for understanding the performance of the
Whisper Room.
When analyzing the audible range transmission loss results, the noise reduction
trends mostly as expected. With the exception of the 60-100 Hz bands, the amount
of reduction generally increases with frequency. This was expected knowing that as
the wavelength of sound approached the wall thickness, more sound would be
attenuated. The contradiction to this trend, occurring primarily in the 80 Hz band,
was attributed to a wall panel structural vibration, as noted previously. Because this
was still outside of the range of primary interest for this project, the source of the
Figure 73: Z-weighted transmission loss measured with white noise at 1/3-octave bands. The transmission loss values are expressed as negative, implying sound reduced. The figure shows an increasing amount of reduction with frequency, which was expected.
-40.00
-30.00
-20.00
-10.00
0.00
10.00
20.00 𝑳𝑳𝑨𝑨𝒆𝒆𝒆𝒆 = −𝟐𝟐𝟐𝟐.𝟏𝟏𝒅𝒅𝒅𝒅
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resonance was not investigated, and the problem was considered insignificant.
When compared to the projected values from the Whisper Room shown in Fig. 64,
the measured results show a slight variation from the specified results. Table 4
shows the compared reduction results.
When comparing the measured and projected results, the Whisper Room performed
comparably to its specifications in the region of interest (300-1500Hz). At low
frequencies, the measurements showed significant underperformance. This was
particularly at low frequencies below the region of interest where discrepancies
upwards of 10 dB were observed. Conversely, the measurements showed significant
overperformance at high frequencies. Again, this occurred primarily in regions
above the frequency region of interest. Within the region of interest, the 500 Hz
band saw identical noise reduction results when compared to the specified results.
Overall, the specifications bred expectations of relatively little variation in noise
isolation over the bands given. The measurements, however, showed a somewhat
linear trend ranging from the net gain amounts in the infrasonic region to around -
40 dB reduction amounts near the peak of the audible region. While the discrepancy
in noise reduction variation was unexpected and disappointing, the Whisper Room’s
isolation capabilities were acceptable over the region of most importance.
Recall that the desired transmission loss buffer room for performing accurate ANC
measurements was 5 dB. Meaning that if an ANC system was producing 10 dB of
cancellation at a specific frequency, the room would need to provide 15 dB of sound
isolation at that frequency. When reviewing the transmission loss results, the
Table 4: Measured sound isolation compared to projected (from Fig. 64) sound isolation at relevant octave bands.
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maximum amount of measurable noise reduction possible using the ANC system in
the Whisper Room was determined. These values are shown for one-third octave
bands from 300-1500 Hz in TBL. 5.
The amount of measurable noise reduction was lower than expected at lower
frequencies. Still, the transmission loss results show that the Whisper Room
provides enough isolation to accurately measure up to 15 dB of noise reduction
using an ANC system across the entire frequency range of interest.
Table 5: Measurable noise cancellation possible using an ANC system in the Whisper Room over the primary frequency range of operation.
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Chapter 6: Concluding Material
6.1 Research Summary This chapter gives a condensed review of the progress made on the project, examines
possible technical improvements, and concludes by discussing project direction and
future work.
6.1.1 Project Foundation
The comprehensive objective of this research project is to develop a functioning
ANC system to globally reduce noise travelling through an open window. While the
prospective of large volume ANC has previously been questioned, recent
technological advancements in digital signal processing have led many to research
its possible applications. At the PSU TDL, Miller developed theoretical models
which predicted the capability of a sparsely distributed speaker array to perform
noise reduction. The array’s noise cancelling performance would be optimized using
an algorithm which prescribes beam forming filters for each driver. The
development of this optimization algorithm was crucial to the future success of the
project. After the algorithm was developed, the focus of the project shifted from
primarily theoretical to experimental research. Miller developed the first iteration of
the array but was unable to obtain experimental results which validated his
theoretical work. Still, Miller’s work was foundational for the TDL’s research on
the subject and generated great optimism for the project’s future.
6.1.2 Array Iteration 2
The second iteration of the array was designed to improve the various problems
associated with the first array and was developed by Miller and Downey. The
redesign saw improved manufacturing design, improved driver distortion
performance, and reduced signal processing load. While this array design
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successfully addressed many problems associated with the first array, several new
issues arose after analyzing the performance results. The primary faults here were
array frame structural vibrations and poor driver frequency responses.
6.1.3 Iteration 3
The third array design, developed by Downey, corrected both primary issues
associated with iteration two. First, the structural resonances were suppressed by
manufacturing a new, thicker array frame. Next, the poor acoustical performance of
the speakers was addressed by adding individual closed-box baffles to the back sides
of the drivers. Adding enclosures prevented back radiation from the speakers and
improved the frequency responses of the drivers dramatically. Additionally, the
equalization process was shown to successfully group and smooth the frequency
responses for each driver set. Overall, the improvements made during the third
iteration development yielded an array substantially more capable of obtaining
quality ANC measurements than all previous designs.
6.1.4 Lab Facility Development
In addition to the development of the secondary source array, the measurement
facilities were also improved significantly. Previously, the facility used for testing
was an anechoic chamber coupled to a reverberant chamber. This location was not
ideal for obtaining global ANC measurements because of the acoustic challenges
associated with using the reverberant chamber. Additionally, the accessibility of the
facility was limited by the primary lab operator. Because of this, a new lab space
was developed which included the construction of a sound isolation chamber. This
chamber was purchased, constructed, and is now run by the TDL. Transmission loss
measurements revealed that ANC reductions of at least 15 dB would be accurately
measurable from 300-1500 Hz using the new chamber.
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6.2 Future Work Several challenges have arisen throughout the life of this research project, and while
many have been successfully resolved, others deemed less immediately relevant
have not. Some of these challenges included signal processing capabilities of
MATLAB and the computers used, the robustness and refinement of the array
design, and continued lack of ideal measurement facilities. This section discusses
some possible solutions to these challenges and seeks to provide some element of
project direction for the future.
6.2.1 MATLAB
Throughout the project history, when attempting to perform multichannel analyses
using MATLAB as the controlling software, signal processing overloads have
plagued the measurements. While the laptop computers used were not ideal for
handling the processing load, MATLAB was often considered the primary source
of overload failure. In response to this, suggestions arose to transition from
MATLAB to Python as the controlling software, specifically for multichannel audio
measurements. However, MathWorks has recently made significant improvements
to the audio signal processing capabilities of MATLAB. This may allow future
researchers to continue using MATLAB for multichannel measurements if
desirable, but understanding these previous challenges is important in the event that
the MATLAB improvements are insufficient.
6.2.2. Array Design Improvements
Next, the array design and construction robustness has been an unaddressed point
of interest for some time. While significant improvements have been made
throughout the project history, continued improvements will be necessary as the
array is developed. The mechanical and acoustical design improvements have
alleviated most problems associated with obtaining quality measurements. The
remaining improvements are smaller and less pertinent to the array’s ANC
performance. Some of these advancements include improving the array wiring
methods, improving the speaker enclosure attachment method, fine tuning the
speaker enclosure design, and replacing underperforming drivers.
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The wiring for the speakers in the array has been relatively unorganized and
aesthetically poor for most design iterations. While the wiring methods are relatively
unimportant for the array’s ability to cancel sound, unorganized wiring has proven
to be an annoyance when setting up for, performing, and tearing down for
measurements. In the latest array design, the leads for all drivers are connected to
individual alligator clips which are then connected to the wires running to the
amplifiers. Using these alligator clips has previously allowed for easier removal of
wires from the array, which was desirable when using temporary measurement
locations. However, with a more permanent location now available, a more
permanent wiring design should also be implemented. Ideally, a new wiring design
would still allow for simple wire disconnections but would be achieved using a more
sophisticated method.
Another improvement to the mechanical design would be to improve the connection
method of the speaker enclosures to the array frame. Currently, the enclosures are
connected to the frame using an adhesive putty. While this adhesive works well for
creating airtight seals and providing a temporary strong bond, the long-term
adhesive capabilities of the material are poor. A more robust, durable solution would
be to connect the enclosures to the frame using screws and some kind of rubber
gasket to form the airtight seal. While revamping this part of the mechanical design
will likely be necessary in the future, quality ANC measurements can be made using
the current design.
Another possible improvement may to fine tune the acoustic design of the speaker
enclosures to obtain more desirable frequency responses. The closed-box baffle
volumes and shapes were chosen based on convenience of manufacturing, not
acoustic design. Tuning the driver frequency responses may be advantageous to the
ANC performance of the system, and one way to do this would be to alter the
enclosure design. Adjusting the volume size and contents (air verses absorptive
material) would allow for some fine tuning of the speaker resonance characteristics.
Custom enclosure designs could be made easily using modern 3-D printing
technology. While the driver responses were currently deemed sufficient for
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obtaining quality ANC results, the responses could still be improved. Additionally,
fine tuning the responses through acoustical design rather than through digital
filtering may reduce the signal processing load for the system.
Lastly, the array design may be improved by replacing some of the speakers.
Through the construction and deconstruction of iterations two and three, some of
the speakers have been handled roughly. Particularly, the interior drivers were press
fit in and out of the arrays several times. While no superficial damage was noticeable
on the drivers, measuring the mechanical and electrical behavior may reveal a need
to replace some speakers. Specifically, impedance and distortion measurements may
reveal information not seen in the frequency responses. While all the speakers in the
array would likely be sufficient for achieving quality ANC measurements, if the
performance can be improved by replacing drivers, they should be replaced.
6.2.4. Further Measurement Facility Improvements
While the measurement facilities used for this research were improved significantly,
more improvements could be made to enhance the ability to measure the ANC
performance of the array. Recall that the ideal measurement facility would be an
anechoic chamber coupled to another anechoic chamber. The presence of reflections
in either the source or receiving room generates challenges for obtaining accurate
noise measurements. The previous measurement facility had both extremes between
the two rooms used. One was an anechoic chamber, the most ideal environment, and
the other was a reverberant chamber, the least ideal environment. The new
measurement facility places both rooms somewhere in between these extremes. The
Whisper Room is anechoic at mid to high frequencies only because of the small
wedge size of the absorptive foam used. The larger room, Room 22, has no
intentional acoustic absorption treatment but is significantly less reverberant than
the reverb chamber.
The new facility could be improved by enhancing the absorptive material to both
rooms. For the Whisper Room, investing in foam panels with larger wedges would
increase the frequency range over which the room is anechoic. This would likely be
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a worthwhile investment, especially if the room is used for other acoustic
measurements. Additionally, inserting any absorptive material into the larger room
would be beneficial, although purchasing acoustic paneling for this room would not
be a worthwhile investment because of its large size. Because ANC measurements
have not yet been performed in the new facility, the extent to which reflections will
negatively impact the results is unknown. Knowing this, improving the
reverberation characteristics of the rooms should be deferred until after the ANC
measurements are analyzed.
If the current measurement facility orientation were to be ineffective for performing
ANC measurements, other options are available using the Whisper Room.
Developing a scale model of the ANC system could be a legitimate second option
for analyzing the theoretical design. Additionally, the sound isolation chamber could
potentially be divided into two spaces, in which case the chamber could replicate
coupled anechoic chambers. While these are legitimate options for back up
measurement facilities, the current facility configuration will be the primary choice.
6.3 Final Conclusions
6.3.1 Results
This project saw significant improvements to the mechanical and acoustical design
of the secondary source array to be used for a large volume ANC system. The
improvements to array included the mitigation of structural resonances and
significant improvements to the frequency responses of the drivers in the array.
Additionally, a new measurement facility was constructed to be used for future ANC
measurements. Between the improvements made to the array design and
measurement facilities, the ability to obtain accurate experimental results which
validate Miller’s theoretical results was improved significantly.
6.3.2 Future Applications
The progress made both by Penn State’s Transducers Development Laboratory and
other leading researchers around the world has led to the legitimate possibility of
future applications for large volume ANC systems. Recent work by the NTU group
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in Singapore made world-wide news in the scientific community and among the
general population. Something that was once deemed an impossibility has become
a reality with the advancements in technology over the years. While the prospective
implementation in the immediate future may still be impractical, applications of
consumer, large volume ANC systems for office spaces, urban housing, and much
more may be on the horizon.
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Appendix A: Speaker Specifications
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Appendix B: Measurement Facility
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The following details the construction process of the Whisper Room and highlights
the features discussed in section 5.1. The section will be presented as a bulleted list
with images for references. This is not a comprehensive instruction manual, but full
assembly instructions are shown in the Whisper Room MDL 96120S/SNV assembly
manual.
1. The first assembly step was to attach numerous wheels to the base structure of the
room. Each wheel was mounted using four screws.
2. After attaching the wheels, the base structure was assembled by connecting three
pieces together using connection brackets. Each connection bracket was attached
using four screws.
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3. After assembling, the base structure was leveled. To check the leveling, a long
bubble level was used on each corner of the base. If not level, shims were added
under the wheels of the base to make as flat as possible.
4. After leveling the base structure, rubber padding was added to provide vibration
isolation for the room from the floor. The rubber sheets were unrolled and laid in
the base frame. The image shows one corner of the base structure with the rubber,
dark colored, padding placed down.
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5. Once the rubber padding was added, the interior flooring was placed on top of the
rubber. The flooring fit snugly in the base frame using the metal dividers to space
the pieces properly.
6. After the floor was assembled, the door frame, first wall piece, and corner were
assembled. The frame was connected using a mounting bracket with several
screws. The images show the mounting bracket and installed corner pieces. The
wall sections were attached to the base using hinged, plastic brackets.
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After the door frame was assembled, the two more sets of walls were assembled
around the back side of the base to form a U shape. The walls were also attached to
each other via connection panels running along the height of the walls. These panels
were on the outside of the wall, so they cannot be seen here
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7. After the section of walls were assembled, the first ceiling panel was attached. The
panel was large, and weighed over 50 pounds, so help was needed for lifting.
Additionally, aligning the holes for the bracket connectors was challenging. Using
a tool to force the holes into alignment was necessary.
8. After the ceiling piece was attached, the wall construction was continued around
the back of the structure. The wall panels on the back and side closest to the camera
were the ventilation panels. In total, three walls were used for ventilation.
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9. After the rest of the ceiling pieces were attached, the only remaining opening was
the window wall panel. This last wall piece was challenging to attached because
of hole alignment problems. Several other panels were not screwed tightly in place
to allow for slight movement. This was necessary to finally aligning the last wall
panel.
10. The last step for the structural assembly was attaching the door. The door was
suspended in its place by sliding pins into the hinges on the door frame.
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11. After the structural assembly was completed, additional accessories were added to
improve the room’s usability. First, the ventilation systems were added. Working
in a room with acoustic foam creates a very dry environment which can be
uncomfortable to be in for long periods of time. The ventilation systems help pump
fresh air into the room. Because fan noise can be quite noisy, silencers were
included in the ventilation package. PERFORM MEASUREMENTS WITH
FANS OFF.
12. After the ventilation system was installed, acoustic foam paneling was added to
the interior of the room. The foam was attached to the walls using Velcro.
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13. Next, lighting units were mounted to the interior of the room. To do this, power
was also run into the room. Two outlet strips were run through the cable ports. The
lighting was then attached to the center of the ceiling using Velcro. Additional
lighting units were added around the perimeter of the ceiling interior to provide a
more thoroughly lit space.
14. After the entire assembly was completed, the latest iteration of the array was
mounted in the window in place of the glass. To do this, the light frame holding
the glass in place was removed, and the array was mounted in its place.
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15. Some additional attachments were included with the assembly. First, MDF panels
were included as replacements for both glass windows. While the window for the
array will likely stay the same, the window in the door could be swapped if desired.
The image shows both MDF window panels in place.
16. The last addition to the structure was a pegboard sheet for organizing cabling.
While this was a non-essential addition, having increased spatial and equipment
organization will improve setup and tear down efficiency.
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Images of the final Whisper Room assembly are shown from the exterior.
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Appendix C: Self Noise Correction All sound pressure level (SPL) measurements taken using the Brüel & Kjær Type
2250 sound level meter were corrected to account for the self-generated noise of the
combined microphone and electrical systems. The self-noise of the system was
provided in the user manual for third octave bands. This figure is shown below, and
values were extracted from plot. The values were estimated to one tenth of a dB.
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Appendix D: Coding Improvements During the Covid-19 pandemic, inaccessibility to the research labs prevented
continuation of measurement-based array evaluations. Despite this major setback,
meaningful progress continued as significant improvements were made to the
MATLAB coding used for performing and analyzing speaker frequency response
measurements. Improvements ranged from improving code workflow, adding new
features, redefining plotting methods, to creating new scripts with the specific
purpose of testing equalization filters. Additionally, a help document was written
explaining the details for operating the measurement code. The ultimate goal of this
work was to improve the usability of Miller’s foundational measurement scripts for
future users. Several elements are included here, including a workflow diagram for
performing and analyzing frequency response measurements and the primary
MATLAB scripts associated with that workflow. The diagram is shown on the next
page with the scripts following.
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This code flow begins by generating the initial measurement signal and ends by
outputting the equalized frequency response of a speaker. The code was written
for both single drivers and multiple drivers depending on the extent of the
measurements being taken. In the diagram, the left-side blocks give the input
files necessary for running the primary scripts. These included either .wav files
or .mat files. The center column of blocks gives the primary .m scripts used
along with any subsidiary functions or controllers within them. The right-side
blocks show the files output from the primary scripts. Again, these were either
.wav or .mat files. The primary scripts are run in order flowing down the chart.
Similar MATLAB scripts can be found presented in Miller’s thesis, but upon
inspection, several adaptations are noticed.
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Write Unfiltered Measurement Signal
%% Write_Signal_One_Driver_Unfiltered % Writes signal for initial, unfiltered, impulse response measurement % First two sections are optional test signals % Last section is measurement signal %% Test signal (for reflections) % clear,clc,close all % fs = 44100; %
sampling freq % % % reps of 1 short chirp with long pause after % test_chp = (create_sweep('EFM',fs,[100 1000],0.02,0.98,0.025,11)).'; %
create a sweep % % % Audiowrite % audiowrite('Genelec_Test_Keagan.wav',test_chp,fs) %
make a wave file out of the signal %% Test Signal - channel matches driver check % clear,clc,close all % % fs = 44100; %
sampling freq % G = 0.03; %
linear gain multiplier % % test_chp = G*create_sweep('EFM',fs,[10 25000],1,0.5,0.025,5); %
create a sweep % test_nz = G*(randn(30*fs,1)); %
white noise % % % Audiowrite % audiowrite('test_nz.wav',test_nz,fs) %
write the noise wave file % audiowrite('test_chp.wav',test_chp,fs) %
write the sweep wave file %% Measurement Signals - 1 chan active at a time clear,clc,close all fs = 44100; %
sampling freq
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G = 0.05; % linear gain Nrep = 20; %
number of reps to play single_chp = G*create_sweep('EFM',fs,[10 25000],1,0,0.025,1); %
create a base chirp/sweep meas_sig = zeros(size(repmat(single_chp.',[Nrep 1]))); %
start with a matrix of zeros meas_sig = repmat(single_chp.',[Nrep 1]); %
Repeat chirps for number of repetitions % Audiowrite audiowrite('Measurement_Signal_Unfiltered.wav',meas_sig,fs)
% write the wave file save('Measurement_Signal_Unfiltered.mat','single_chp','Nrep','fs','meas_sig')
% save the variables to be used in get_meas_IR.m
Run Unfiltered Measurements
%% IR_Measurement_Control_Script_Unfiltered % One Driver clc,close all clear % Opens and runs simulink model to play/record for unfiltered signal % % NOTE: ensure proper wav file is selected in simulink % model and ensure that proper array speaker is playing before measuring! % % NOTE: ensure that proper input sweep (line 30) is a SINGLE sweep and has the
exact % same properties as those used in chain for measurement signal. This is % changed in the write signal .m file % % DO A CHANNEL CHECK BEFORE MEASURING % Inputs T = 21; % duration of simulink (if
simulink run time set to 'T') device = 'Genelec_Unfiltered'; % for file naming when data
is saved
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% Run simulink file model = 'Measurement_Controller_Unfiltered.slx'; % Simulink model filename load_system(model); % load the simulink model
from main script disp('Running simulink') % Notify user of
commencement sim(model) % run the simulink file disp('Simulink done') % Notify user of
termination % Inputs for get_meas_IR.m load 'Measurement_Signal_Unfiltered.mat' % brings back up properties
of the input signal data = micdata.'; % rename micdata and switch
row to column or vice versa load BNL_13Nov.mat % loads BNL associated
variables BNL_data = micdata; % rename micdata clear micdata % get rid of micdata
variable HP_Cutoff = 100; % High Pass Filter Cutoff
Frequency BNL_Choice = 0; % Plot TF with background
noise or not 1=yes,0=no [ir,tf] = IR_Processing(BNL_data,single_chp,data,Nrep,fs,HP_Cutoff,BNL_Choice);
% call IR calc function (see function file for info) %% Saving filename = sprintf('Genelec_TF_Data_Unfiltered.mat',device); save(filename) % save the data
Process Response Data and Write EQ Filters
clear,clc,close all % Write EQ Filter % This file is designed to read, process, and write an EQ filter for data % from a single driver with data collected via our lab's code. %% Read measured data
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% Open files and extract IR / TF for 1 driver names = 1; load('Genelec_TF_Data_Unfiltered.mat') % load the
current data file IR_raw = ir; % store raw
IR TF_raw = tf; % store raw
TF %% Input Parameters align_t_ms = 5; % time at
which IR spikes will be aligned [ms] fs = 44100; % sampling
rate dt = 1/fs; % time
differential [s] N = length(ir); % number of
points in time signal T = N*dt; % Time of
signal [s] df = fs/length(ir); % frequency
differential [Hz] TIR = 200; % time
duration of impulse repsonse [ms] hL = 250; % length in
samples of hanning window used to taper the signal GdB = -5; % amount of
gain to apply to the end result EQ filters smooth_n = 100; % input for
median smoothing routine (with non-peaking responses this entire section of code below won't be necessary) align_N = round(fs*align_t_ms/1000); % sample at
which IR spikes will be aligned Time = ((0:N-1)*dt).'; % Time
vector Freq = ((0:fs/2)*df).'; % Frequency
vector %% Circshift so all IRs align [~,ind] = max(abs(IR_raw)); % find the
indices where each IR spikes for bb = 1:length(names)
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IRs_aligned(:,bb) = circshift(IR_raw(:,bb),-(ind(bb)-align_N-1),1); % circshift the IRs so that they align at specified time (applying a pure delay to the impulse response) end TFs_aligned = fft(IRs_aligned)/fs; %
recalculate the transfer functions after the IRs have been delayed % % Plot to Check Aligned Impulse Responses % figure % plot(Time,IRs_aligned) % hold on % xlabel('Time (s)') % ylabel('Amplitude') % title('Shifted Impulse Response') %% Window Imp Resp to remove unwanted information tpr_begin_t_ms = align_t_ms + TIR; % time in
ms along duration of full IR at which taper begins tpr_begin_N = round(fs*tpr_begin_t_ms/1000); % above
time but in sample tpr = hann(hL); tpr = tpr((round((hL-1)/2,0)):end); % create a
hanning window to use as taper (only take the back half) tpr_fcn = ones(fs,1); % create a
taper function vector and preallocate with ones tpr_fcn(tpr_begin_N:tpr_begin_N+length(tpr)-1) = tpr; % fill in
the taper function vector with the hanning window tpr_fcn(tpr_begin_N+length(tpr):end) = 0; % fill in
the rest of taper function vector with zeros tpr_fcn(1:length(tpr)) = flipud(tpr); % fill in
the beginning of the taper function with the flipped version (tapers into the IR too) % Compute Shifted IRs and TFs IRs = IRs_aligned .* repmat(tpr_fcn,[1 length(names) 1]); % multiply
the IRs by the taper function TFs = fft(IRs)/fs; % again
recalc the TFs % % Plot to Check Aligned, Tapered Impulse Responses with Window % figure % yyaxis left % plot(Time,IRs,'-') % hold on % yyaxis right % plot(Time,tpr_fcn,'r')
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% xlabel('Time (s)') % ylabel('Amplitude') % title('Impulse Response with Window') %% Frequency Response Plots Mag = 10*log10(abs(TFs(1:fs/2+1))/abs(max(TFs))); % Magnitude of
TF Ph = unwrap(angle(TFs(1:fs/2+1))*180/pi); % Phase of TF % Plot Magnitude figure semilogx(Freq,Mag,'k','linewidth',1.5) xlabel('Frequency [Hz]') ylabel('Magnitude (dB ref: Max(TFs))') title('Frequency Response: Magnitude') xlim([50 20000]) ylim([-50 25]) % Plot Phase figure plot(Freq,Ph,'k','linewidth',1.5) xlabel('Frequency [Hz]') ylabel('Phase (Deg)') title('Frequency Response: Phase') xlim([50 20000]) %% EQ filters - this part of the code writes the EQ filters based on the above
prepared driver responses % Approximate inverse of TFs TFs_inv = (TFs + eps).^-1; % inverse
driver TF Mag_inv = 10*log10(abs(TFs_inv(1:fs/2+1))/abs(min(TFs_inv))); % Magnitude
of TF % % Plot original * inverse (should be zero at all frequencies) % figure % semilogx(db(abs(TFs.*TFs_inv))) % xlabel('Frequency [Hz]') % ylabel('Magnitude (dB ref: 1)') % title('Original*Inverse TFs'); % ylim([-30 30]) % Plots response and inverse on same plot (should mirror about x-axis) figure; semilogx(Freq,Mag,'k')
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hold on; semilogx(Freq,Mag_inv,'r') xlabel('Frequency [Hz]') ylabel('Magnitude (dB ref: Max(TFs), Min(TFs_inv))') title('Original and Inverse Response Magnitudes') legend('Original Response','Inverted Response') % FIR band pass to roll off responses at high and low ends f1 = 150; % low end cut
off freq f2 = 17500; % high end cut
off freq N = 4096; % number of
taps fs = 44100; % sampling freq freq_norm = [f1 f2]/(fs/2); % normalized
cut off freqs b = fir1(N,freq_norm); % matlab
function: Window-based FIR filter design [HBP,hBP] = test_filter(b,1,fs,T); % run test
filter function and extract responses % Plot BP and all raw TFs to determine how to adjust filters % Linear gain modifier added if needed! Can adjust here in plot line % to find right amount and adjust in the input section to alter overall EQ figure semilogx(0:22050,db(abs(HBP(1:22051))),'y-.','linewidth',2); hold on % plot
the band pass TF semilogx(Freq,Mag) % plot
the driver TFs semilogx(0:22050,-3+db(abs(HBP(1:22051))),'g-.','linewidth',1); % plot
the band pass TF with negative gain applied so visual judgement can be made set(gca,'color','k') % plot
settings xlabel('Frequency [Hz]') ylabel('Magnitude (dB ref: Max(TFs))') title('Filter Check') xlim([20 10000]); hold off % plot
settings % Cascade the two filter responses into EQ filter response G = db2mag(GdB); % calc
linear gain from db EQ_filt_array_TFs = G * TFs_inv .* HBP; % get
EQ filter response (TFs)
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EQ_filt_array_IRs = ifft(EQ_filt_array_TFs)*fs; % get EQ filter IRs % % Plot Impulse Response of total filter % figure % plot(EQ_filt_array_IRs,'k') % xlabel('time [s]') % ylabel('Amplitude') % title('Total Filter IR') %% Compute combined filter frequency response Mag_filt =
10*log10(abs(EQ_filt_array_TFs(1:fs/2+1))/abs(max(EQ_filt_array_TFs))); % Magnitude of Total Filter Ph_filt = unwrap(angle(EQ_filt_array_TFs(1:fs/2+1))*180/pi);
% Phase of Total Filter % Plot Total Filter Magnitude figure semilogx(Freq,Mag_filt,'k') xlabel('Frequency [Hz]') ylabel('Magnitude (dB ref: Max(Filter)') title('Total Filter Response: Magnitude') ylim([-100 50]) % % % Plot Total Filter Phase % figure % plot(Freq,Ph_filt,'r') % xlabel('Frequency [Hz]') % ylabel('Phase (Deg)') % title('Total Filter Response: Phase') %% Corrected TF functions % Applies total filter to measured signal to give THEORETICAL Filtered % Response TFs_corr = TFs .* EQ_filt_array_TFs; %
multiply the driver TFs by the EQ filter TFs to filter the reponses: should produce ideal response TFM = abs(max(TFs_corr)); % Max
value of corrected TF Mag_corr = 10*log10(abs(TFs_corr(1:fs/2+1))/TFM(1)); %
Magnitude of TF Ph_corr = unwrap(angle(TFs_corr(1:fs/2+1))*180/pi); % Phase
of TF % Plot Magnitude
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figure semilogx(Freq,Mag_corr) xlabel('Frequency [Hz]') ylabel('Magnitude (dB ref: Max(TFs))') title('Filtered Response: Magnitude') xlim([50 20000]) ylim([-80 10]) % Plot Phase figure plot(Freq,Ph_corr) xlabel('Frequency [Hz]') ylabel('Phase (Deg)') title('Filtered Response: Phase') xlim([50 10000]) %% Save EQ Filter save('EQ_Filter_Genelec.mat','EQ_filt_array_TFs','Freq')
Write Filtered Measurement Signals
%% Write_Signal_One_Driver_Filtered clear,clc,close all %% Measurement Signals - 1 chan active at a time load 'EQ_Filter_Genelec.mat'
% load EQ Filter data fs = 44100;
% sampling freq G = 0.05;
% linear gain Nrep = 20;
% number of reps to play % Creates Single Chirp and Filters single_chp = G*create_sweep('EFM',fs,[10 25000],1,0,0.025,1).';
% create a base chirp/sweep single_chp_freq = fft(single_chp)/fs;
% FFT of chirp single_chp_filtered = single_chp_freq .* EQ_filt_array_TFs;
% Filter chirp % Back to time domain
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single_chp_filtered = ifft(single_chp_filtered)*fs; % Back to time domain via ifft meas_sig = zeros(size(repmat(single_chp_filtered.',[Nrep 1])));
% start with a matrix of zeros meas_sig = repmat(single_chp_filtered,[Nrep 1]); %
Repeat chirps for number of repetitions figure plot(single_chp,'k') hold on plot(single_chp_filtered) xlabel('Samples [n]') ylabel('Amplitude') title('Input Signal Comparison') legend('Unfiltered','Filtered') % Audiowrite % KEY NOTE - In order to compute to filtered response correctly, make sure % to export the filtered signal for simulink, but the unfiltered single % chirp for the control script. When computing the transfer function in the % processing function, the measured signal is to be compared to the % unfiltered chirp, not the filtered chirp. single_chp = (single_chp).';
% Back to time domain via ifft audiowrite('Measurement_Signal_Filtered.wav',meas_sig,fs)
% write the wave file save('Measurement_Signal_Filtered.mat','single_chp','Nrep','fs','meas_sig')
% save the variables to be used in get_meas_IR.m
Run Filtered Measurements
%% IR_Measurement_Control_Script_Filtered clc,close all clear % Opens and runs simulink model to play/record % % NOTE: ensure proper wav file is selected in simulink % model and ensure that proper array speaker is playing before measuring!! %
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% NOTE: ensure that proper input sweep (line 30) is a SINGLE sweep and has the exact % same properties as those used in chain for measurement signal % % DO A CHANNEL CHECK BEFORE MEASURING % Inputs T = 22; % duration of simulink (if
simulink run time set to 'T') device = 'Genelec_Filtered'; % for file naming when data
is saved % Run simulink file model = 'Measurement_Controller_Filtered.slx'; % Simulink model filename load_system(model); % load the simulink model
from main script disp('Running simulink') % Notify user of
commencement sim(model) % run the simulink file disp('Simulink done') % Notify user of
termination % Inputs for get_meas_IR.m load 'Measurement_Signal_Filtered.mat' % brings back up properties
of the input signal data = micdata.'; % rename micdata and switch
row to column or vice versa load BNL_13Nov.mat % loads BNL associated
variables BNL_data = micdata; % rename micdata clear micdata % get rid of micdata
variable HP_Cutoff = 100; % High Pass Filter Cutoff
Frequency BNL_Choice = 0; % Plot TF with background
noise or not 1=yes,0=no [ir,tf] = IR_Processing(BNL_data,single_chp,data,Nrep,fs,HP_Cutoff,BNL_Choice);
% call IR calc function (see function file for info) %% Saving filename = sprintf('Genelec_TF_Data_Filtered.mat',device); save(filename) % save the data
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Additional*: Response Comparison File
This script was used for comparing measurement results from several different
array designs. It was used to compare both unfiltered and filtered results. Nearly
all figures presented in this paper were generated by this file or a variation of
this file.
clear,clc,close all % Response Comparison File % This file is import all EQd response data, generate frequency response plots, % and compare %% Read measured data % Open files and extract IRs / TFs, storing all data in one array % Lane and Keagan 2 Data str1 = 'data_ch*.mat'; % string
to catch files with matching names str2 = 'Ldata_ch*.mat'; % string
to catch files with matching names s1 = dir(str1); %
structure containing all files that matched str s2 = dir(str2); %
structure containing all files that matched str names1 = {s1.name}.'; % cell of
file names from s - check to make sure you got what you intended names2 = {s2.name}.'; % cell of
file names from s - check to make sure you got what you intended for j = 1:length(names1) % for all
the data files matching str load(names1{j}) % load the
current data file IR_raw1(:,j) = ir; % store
raw IRs TF_raw1(:,j) = tf; % store
raw TFs end for i = 1:length(names2) % for all
the data files matching str load(names2{i}) % load the
current data file
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IR_raw2(:,i) = ir; % store raw IRs TF_raw2(:,i) = tf; % store
raw TFs end % Keagan 1 Data ZZ = importdata('measured_ir_data_sort.mat'); %
Import Data File n = size(ZZ,1); %
Number of drivers Time_App = ZZ.ImpulseResponse(1).Time; %
Extract Time vector from app Freq_App = ZZ.MagnitudeResponse(1).Frequency; %
Extract Frequency vector from app for i = 1:n Mag_App(:,i) = ZZ.MagnitudeResponse(i).PowerDb; %
Extract all frequency response magnitudes (dB) Ph_App(:,i) = ZZ.PhaseResponse(i).Phase; %
Extract all frequency response phases (rad) Imp_1(:,i) = ZZ.ImpulseResponse(i).Amplitude; %
Extract all impulse responses % Note: Will need to zero Pad Impulse to correct length if MATLAB App % differs from our sweep (length 1 second) have to change depending on % MATLAB App settings). Currently, the script is set up to work for % setting the default length in the MATLAB App (the little slider) to 1 % second. That makes a 0.5 second sweep with a longer pause. In the % end, you just need to make sure the filter and sweep can be % multiplied in the frequency domain in the write filtered signal file. % This means they must be the same length. Remember, zero padding in % the time domain doesn't change your frequency data, only resolution. IR_raw3(:,i) = [Imp_1(:,i) ; zeros(length(Imp_1(:,i)),1)]; end fs = 44100; %
Sample Rate [Hz] TF_raw3 = fft(IR_raw3)/fs;
% Computes original Transfer Function %% Input Parameters align_t_ms = 5; % time at
which IR spikes will be aligned fs = 44100; % sampling
rate dt = 1/fs; % time
differential [s]
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N = length(ir); % number of points in time signal T = N*dt; df = fs/length(ir); % frequency
differential [Hz] TIR = 200; % time
duration of impulse repsonse in ms hL = 250; % length in
samples of hanning window used to taper the signal GdB = 0; % amount of
gain to apply to the end result EQ filters smooth_n = 100; % input for
median smoothing routine (with non-peaking responses this entire section of code below won't be necessary) align_N = round(fs*align_t_ms/1000); % sample at
which IR spikes will be aligned Time = ((0:N-1)*dt).'; % Time
vector Freq = ((0:fs/2)*df).'; % Frequency
vector %% Circshift so all IRs align [~,ind1] = max(abs(IR_raw1)); % find
the indices where each IR spikes [~,ind2] = max(abs(IR_raw2)); [~,ind3] = max(abs(IR_raw3)); for bb = 1:length(names1) IRs_aligned1(:,bb) = circshift(IR_raw1(:,bb),-(ind1(bb)-align_N-1),1); %
circshift the IRs so that they align at specified time (applying a pure delay to the impulse response) IRs_aligned2(:,bb) = circshift(IR_raw2(:,bb),-(ind2(bb)-align_N-1),1); IRs_aligned3(:,bb) = circshift(IR_raw3(:,bb),-(ind3(bb)-align_N-1),1); end TFs_aligned1 = fft(IRs_aligned1)/fs; %
recalculate the transfer functions after the IRs have been delayed TFs_aligned2 = fft(IRs_aligned2)/fs; TFs_aligned3 = fft(IRs_aligned3)/fs; % % Plot to Check Aligned Impulse Responses % figure % for i = 1:length(names) % plot(Time,IRs_aligned1(:,i)) % hold on % xlabel('Time (s)') % ylabel('Amplitude') % title('Shifted Impulse Responses')
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% end %% Window Imp Resp to remove unwanted information tpr_begin_t_ms = align_t_ms + TIR; % time in
ms along duration of full IR at which taper begins tpr_begin_N = round(fs*tpr_begin_t_ms/1000); % above
time but in sample tpr = hann(hL); tpr = tpr((round((hL-1)/2,0)):end); % create a
hanning window to use as taper (only take the back half) tpr_fcn = ones(fs,1); % create a
taper function vector and preallocate with ones tpr_fcn(tpr_begin_N:tpr_begin_N+length(tpr)-1) = tpr; % fill in
the taper function vector with the hanning window tpr_fcn(tpr_begin_N+length(tpr):end) = 0; % fill in
the rest of taper function vector with zeros tpr_fcn(1:length(tpr)) = flipud(tpr); % fill in
the beginning of the taper function with the flipped version (tapers into the IR too) % Compute Shifted IRs and TFs IRs1 = IRs_aligned1 .* repmat(tpr_fcn,[1 length(names1) 1]); % multiply
the IRs by the taper function IRs2 = IRs_aligned2 .* repmat(tpr_fcn,[1 length(names1) 1]); IRs3 = IRs_aligned3 .* repmat(tpr_fcn,[1 length(names1) 1]); TFs1 = fft(IRs1)/fs; % again
recalc the TFs TFs2 = fft(IRs2)/fs; TFs3 = fft(IRs3)/fs; % % Plot to Check Aligned, Tapered Impulse Responses with Window % figure % yyaxis left % plot(Time,IRs1) % hold on % yyaxis right % plot(Time,tpr_fcn,'r') % xlabel('Time (s)') % ylabel('Amplitude') % title('Impulse Responses with Window') %% Frequency Response Plots for i = 1:length(names1) Mag1(:,i) = 10*log10(abs(TFs1(1:fs/2+1,i))/abs(max(TFs1(:,i)))); %
Magnitude of TF Mag2(:,i) = 10*log10(abs(TFs2(1:fs/2+1,i))/abs(max(TFs2(:,i)))); Mag3(:,i) = 10*log10(abs(TFs3(1:fs/2+1,i))/abs(max(TFs3(:,i))));
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Ph1(:,i) = unwrap(angle(TFs1(1:fs/2+1,i))*180/pi); % Phase of TF Ph2(:,i) = unwrap(angle(TFs2(1:fs/2+1,i))*180/pi); Ph3(:,i) = unwrap(angle(TFs3(1:fs/2+1,i))*180/pi); end % % Plot Magnitude % for i = 1:length(names1) % figure % semilogx(Freq,Mag1(:,i),'k','linewidth',1.5) % hold % semilogx(Freq,Mag2(:,i),'r','linewidth',1.5) % semilogx(Freq,Mag3(:,i),'b','linewidth',1.5) % xlabel('Frequency [Hz]') % ylabel('Magnitude (dB ref: Max(TFs))') % title(['Frequency Response Driver ',sprintf('%d',i),': Magnitude']) % xlim([50 20000]) % ylim([-40 10]) % end % % % Plot Phase % for i = 1:length(names) % figure % plot(Freq,Ph1(:,i),'k','linewidth',1.5) % plot(Freq,Ph2(:,i),'r','linewidth',1.5) % plot(Freq,Ph3(:,i),'b','linewidth',1.5) % xlabel('Frequency [Hz]') % ylabel('Phase (Deg)') % title(['Frequency Response Driver ',sprintf('%d',i),': Phase']) % xlim([50 20000]) % end % Plot responses together by group group1 = [1:9]; %
Channels of interest % Magnitude figure M1 = semilogx(Freq,Mag1(:,group1),'k'); hold on %M2 = semilogx(Freq,Mag2(:,group1),'b'); % LTSpice j = sqrt(-1); Mag = sqrt(Real.^2+Imag.^2); Mag_LT = 10*log10(abs(Mag)/abs(max(Mag))); M3 = semilogx(Freq1,Mag_LT,'g','LineWidth',2);
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% Mag2 = sqrt(Real2.^2+Imag2.^2); % Mag_LT2 = 10*log10(abs(Mag2)/abs(max(Mag2))); % M4 = semilogx(Freq1,Mag_LT2,'m','LineWidth',2); [~,hObj] = legend([M1(1) M3(1)],{'With Back Volumes','LTSpice Model'}); hL=findobj(hObj,'type','line'); set(hL,'linewidth',1.5) x1 = xline(200,'r','linewidth',1.5); x2 = xline(2000,'r','linewidth',1.5); set(get(get(x1,'Annotation'),'LegendInformation'),'IconDisplayStyle','off'); set(get(get(x2,'Annotation'),'LegendInformation'),'IconDisplayStyle','off'); xlabel('Frequency [Hz]') ylabel('Magnitude (dB ref: Max(TFs))') title('Tang Band Driver LTSpice Model Comparison') xlim([20 20000]) ylim([-30 10]) % % Plot responses together by group % group2 = [6:9]; %
Channels of interest % % Magnitude % figure % semilogx(Freq,Mag1(:,group2),'k') % % hold on % % semilogx(Freq,Mag2(:,group2),'b') % xline(200,'r','linewidth',1.5) % xline(2000,'r','linewidth',1.5) % xlabel('Frequency [Hz]') % ylabel('Magnitude (dB ref: Max(TFs))') % title('Exterior Driver Frequency Responses: Magnitude') % xlim([100 5000]) % ylim([-30 10]) % % Phase % figure % plot(Freq,Ph(:,group)) % hold on % xlabel('Frequency [Hz]') % ylabel('Phase (Deg)') % % title(['Freqency Response Ch ' num2str(group) ' : Phase']) % % title('Exterior Speakers Frequency Response: Phase') % xlim([20 20000])
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