PhD.Thesis:Prediction of sound radiation from structures to assess percpective

PR VISION DU BRUIT RAYONN PAR LES STRUCTURES EN VUE D'UNE VALUATION PERCEPTIVEHiroko Shiraiwa

ENST D partement TSI Groupe AAO Supervisor: Antoine Chaigne 21 juillet 1999

AcknowledgmentsFirst of all, I would like to sincerely thank my supervisor, Antoine Chaigne. I cannot express enough my full gratitude to him. He gave me the opportunity to work in this project, and has guided my study in France through one year. His advice was always precise, proper and appreciated. I appreciate the help of the collaborators, Nacer Hamzaoui and Stephen McAdams. I am glad that I worked with these experienced researchers. Natasa Topalovic has always helped me for precise information and discussion. I was very inspired by her demonstration of perception tests. With Mitsuko Kono, I had long, fruitful and educational discussion about signal processing and mathematics through international phone line. I also cannot forget the help of G lika Papp for her technical advice in signal processing and in writing this report. Doctoral students in the acoustics laboratory, Cyril Touz , David Heleschewitz, and Olivier Thomas, have answered any of my numerous questions during one year. Finally I would like to appreciate two Japanese professors. Shinji Maeda introduced the acoustics laboratory at ENST to me. He also patiently checked this report for better organization and expressions. Kenshi Kishi, my supervisor in University of Electro-Communications in Japan, kindly accepted and encouraged my extra one year study in France.

4

ContentsGlossary of symbols 1 Introduction1.1 Aim of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Role of participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 2.2 2.3 2.4 2.5 DFT representation . . . . . . . . . . . . . . Useful properties of DFT . . . . . . . . . . Frequency response and impulse response . Filtering and linear convolution . . . . . . . FIR lter design by Kaiser window method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iii 11 1

2 Review of signal processing techniques

33 4 5 5 6

3 General information

3.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Simulation and experiment . . . . . . . . . . . . . . . . . . . . . . . 3.3 Description of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 10 10

9

4 Practical procedures

4.1 Data style of the functions . . . . . . . . . . . 4.2 Simulation model . . . . . . . . . . . . . . . . 4.2.1 Transmitted data le . . . . . . . . . . 4.2.2 Getting an impulse response . . . . . . 4.2.3 Synthesis . . . . . . . . . . . . . . . . 4.3 Experiment . . . . . . . . . . . . . . . . . . . 4.3.1 Transmitted data le . . . . . . . . . . 4.3.2 Filtering experimental sound pressure . . . . . . . . . . . . . . . . . . . . . . . .

1515 16 16 16 19 19 19 20

5 Preparation for psychoacoustical tests5.1 Listening tests and required stimuli 5.2 Sound les . . . . . . . . . . . . . . 5.2.1 Format of sound le . . . . 5.2.2 Windowing of the sounds . i

2323 24 24 24

Conclusion

Summary of obtained signals . . . . . . . . . . . . . . . . . . . . . . . . . Comments on spectra of the signals . . . . . . . . . . . . . . . . . . . . . .

2525 25

Bibliography A Program list B Index of signals C Waveforms and spectra of signals

27 29 33 37

ii

Glossary of symbolst ! n k x y h X Y H N MTime (continuous) Normalized radian frequency (continuous) Integer number for functions in time domain Integer number for functions in frequency domain Input in time domain Output in time domain Impulse response Input in frequency domain Output in frequency domain Frequency response Length of sequence (e.g. x n] length)

0 n N 1 has length N.) Order of FIR lter (e.g. an FIR lter H m] 0 m M has M-order, M +1

A Sidelobe amplitude of a lterShape parameter for Kaiser window

fs Sampling frequency fN Nyquist frequency fm Maximum frequency contained in a signal f n] Force which vibrates the plate (input) p n] Sound pressure at a listening point ps n] Synthesized sound pressure pe n] Experimental sound pressureiii

Ps k] Pe k] hp n] hps n] Hps k]

DFT of the synthesized sound pressure DFT of the experimental sound pressure Impulse response of the plate Simulated impulse response of the plate Simulated transfer function of the plate

iv

Chapter 1

Introduction1.1 Aim of the projectHow do human beings perceive sounds? To tackle this question, we try to investigate relationship between two aspects of a sound: Physical parameters and judgment of listeners. First we posturate a simple situation which permits both experiment and simulation: A square plate in free space, ba ed and having one layer, set into vibration by a force at one small point. This simple situation enables us to analyze the physical parameters and to simulate the vibration. Also sound pressure emitted by a real square plate can be recorded in experiments. Perception tests were done for the simulated and experimental sounds to gather judgments of listeners. Second, we focus our attention at sounds generated by a motor, becuase motor noise is one of the most familiar environmental sounds in modern society. The simulation used nit element method in terms of transfer function (pressure=force) of the plate, which is converted into impulse response by the inverse Fourier transform. Experiments were done to record the motor force and sound pressure in an anechoic room. Thus we obtain the experimental sound pressure, and simulated sound pressure which is a linear convolution product of the motor force and of the simulated impulse response. The psychoacoustical analysis is done using multidimensional scaling techniques.

1.2 Role of participantsActual procedures of the project are shared by research groups at three institutes; LVA at INSA de Lyon, group AAO at ENST, and Perception et Cognition Musicale laboratory at IRCAM. This is illustrated in Figure 1.1. 1

INSA took the part of simulation, measurement of forces, and recording of sounds in experiments. ENST worked on signal processing: computation of impulse responses, synthesis of the sounds and preparation of stimuli for psychoacoustical tests including formatting out sound les. IRCAM organized the psychoacoustical tests and analysis of the data.INSA de LYON

Measurement of force Recording of sound pressure Simulation of transfer function (pressure/force)

ENST

Computation of impulse response Synthesis of sounds Preparation of stimuli for psychoacoustical test

IRCAM

Organization of psychoacoustical test Analysis by multidimensional scaling techniques

institutes.

Figure 1.1: Illustration of the joint project: The whole work was organized by the three

2

Chapter 2

Review of signal processing techniques2.1 DFT representationWhen a continuous signal x(t) having maximum frequency fm is processed in a linear time-invariant discrete-time system, x(t) is sampled into sequences of numbers. Sampling frequency fs must exceed the double of fm , i.e. fs 2fm . The Nyquist frequency is given as fN = fs=2 1]. A sequence x, which has its nth element x n], can be represented by normalized radian frequency !, in terms of Fourier representation as,1 j! ) = X x n]e j!n ; X(e n= 1

(2.1)

and

Equation 2.1 is referred as the discrete-time Fourier transform while Equation 2.2 is referred as the inverse discrete-time Fourier transform. In actual calculation, it is more convenient that x n] has a nite length. Thus Fourier representation of nite-duration sequences is di erently de ned. For a periodic sequence x n] with period N, such as ~

x n] = 21

Z

X(ej! )ej!n d!:

(2.2)

x n] = ~(

1 Xr= 1

x n + rN];

a nite-length sequence x n] is written by

x ~ 0nN x n] = 0; n]; otherwise. 1;3

Using a notation WN , which is de ned by

WN = e

j(2 =N) ;

the discrete Fourier transform (DFT), and the inverse DFT (IDFT) of the nitelength sequence x n] become respectively,

X k] =and

N1 X n=0 N1 X k=0

kn x n]WN ;

(2.3) (2.4)

1 x n] = N ~ X k] =

X k]WN kn:

~ Remark that X k] is a part of a periodic sequence X k] with period N;1 Xr= 1

X k + rN]:

To shorten the computation of DFT, FFT (fast Fourier transform) algorithm can be used.

2.2 Useful properties of DFTSince the DFT is an extension of the Fourier transform, the most of Fourier transform properties are still valid. We introduce the two of them. An important property is time-shifting (phase delay). For x n] and its DFT X k], the time-shifting of x n] is obtained by phase delay of X k]. That is, for shifting q samples of sequence x n], the DFT pair iskq x n q] () WN X k]:

(2.5)

The other important property is conjugate-symmetry. When x n] is real number, the DFT is conjugate-symmetric. That is

X k] = X N k 1]:

(2.6)

4

2.3 Frequency response and impulse responseLet X(!); Y (!); and H(!) be Fourier transform of, respectively, x n]; y n]; and h n] such as,

x n] () X(!) (2.7) y n] () Y (!) h n] () H(!): x n] is input while y n] is output. Then h n] is called the impulse response of a lter, and H(!) is called the frequency response. Then the output becomes theconvolution of the inputand the impulse response as

Sequence

Fourier transform

y n] = h n] x n];or

(2.8)

by

(2.9) The frequency response is often represented in its decibel value, which is given

Y (!) = H(!)X(!):

H(!) = 20log10 jH(!)j dB:

(2.10)

2.4 Filtering and linear convolutionM-order nite impulse response (FIR) ltering of a sequence having length N is de ned in the frequency domain by z-transform

Y (z) = h(0) + h(1)z 1 +or in time domain by di erence equation

+ h(M)z

M

X(z);

(2.11)

y n] = h 0]x n] + h 1]x n 1] + M X = h m]x n m];where 0 n N 1. If n varies 0 n N +M point DFTm=0

+ h M]x n M]

(2.12)

1, Eq.2.12 is called a linear convolution. Using N +M 1X k] = H k] =N+M X n=0 N+M X n=01

nk x n]WM+N

1

1

nk h n]WM+N 1 ;

5

linear convolution y n] is also calculated in the frequency domain by

1 y n] = N + M 1

N+M 2 h X k=0

nk H k]X k] WM+N 1 :

i

(2.13)

The computation of a linear convolution of a whole long sequence, i.e. a signal is often too large to be practical. To operate it faster, a breaking-sequence technique becomes e ective. The sequence is separated into small segments, then each segment is linearly convolved in the frequency domain using an overlap-add method 2]. Finally those partial convolutions are connected into an entire convolution. If the segment length is chosen proper, the computation will be carried more rapidly by FFT algorithm.

2.5 FIR lter design by Kaiser window methodAmong numerous methods to design FIR lter, Kaiser window method was used in the procedures. An ideal M-order low-pass lter is recursive with in nite length, such as Using window function w n] of length M +1, an M-order FIR lter is de ned by

M=2)] hlp n] = sin wc (n M=2) ; (n

1 n 1:

h n] = w n]hlp n] 0 n M (2.14) A Kaiser window, w n] with M + 1 length, is designed by following way: Let A(dB) be a desired sidelobes amplitude decrease, and ! be a desired transition width. Then the window length M + 1 and the shape parameter are de ned by A M = 2:285 8! ; 8 > 0:1102(A 8:7); A > 50 < = > 0:5842(A 21)0:4 + 0:07886(A 21); 21 A 50; : 0:0 A < 21: Using those parameters, w n] is given by

kind.

0; otherwise, where = M=2; and I ( ) is the zeroth-order modi ed Bessel function of the rst0 0

8 > < w n] = > :

I0 (1

(n

)= ] ) ] ; 0 n M; I( )2 1=2

(2.15)

6

Thus, following Seq.2.14, an M-order FIR low-pass lter by Kaiser window method is obtained as8 > > > < h n] = > > > :

sin!c(n ) I (1 (n )= ] ) ] ; 0 n M; (n ) I( ) 0; otherwise0 2 1=2 0

(2.16)

7

8

Chapter 3

General information3.1 ConceptThink of a ba ed plate in free space. The plate is a monolithic steel plate having 0.6 m in height, 0.4 m in width and 1.5 mm in thickness. The plate is set in vibration by force f(t) (input). A point where the force is given to the plate is called an excitation point. A point apart from the plate is set as a listening point. Sound pressure at the listening point is referred as p(t).

f(t)Force

p(t)

Figure 3.1: Force f(t) (input) and sound pressure p(t) (output)

f(t) and p(t) are sampled into N-length sequence f n] and p n], for 0 n N 1, by a sampling frequency fs. Since the acoustic behavior of the plate can be assumed to be a time-invariant linear system, the recorded sound, p n], can be described as the output of the lter speci ed by its impulse response hp n] as shown in Figure 3.2. The input to the lter is the force f n]. The sound can be calculated as the convolution between the impulse response and the force as p n] = hp n] f n];9 (3.1)

f[n]

hp[n]

p[n]

Figure 3.2: Illustration of the impulse response: Sound pressure p n] is generated by theforce f n], then call the impulse response of the plate hp n].

and (3.2) Since DFT is used for actual procedures, the DFT of hp n], Hp k], is de ned as the transfer function in the frequency domain.

P(!) = Hp(!)F(!):

3.2 Simulation and experimentForce f n] and sound pressure pe n] were measured in series of experiment at INSA de Lyon. A simulated transfer function hps n] was theoretically established using nite element method as mentioned formerly. Convoluting measured force f n] and simulated impulse response hps n], we obtain synthesized sound pressure ps n]. That is, ps n] = hps n] f n]: (3.3) Thus ps n] and pe n] can be compared in psychoacoustical procedures. At the same time, we intended that experimental impulse response hpe n] can be computed, such as pe n] = hpe n] f n] (3.4) This is for the interest in the frequency domain analysis between Hpe k] and Hps k], which can be done without psychoacoustical procedures. Unfortunately hpe n] was not obtained because pe n] and f n] were not recorded at the same time.

3.3 Description of parametersFollowing parameters are varied for hp n] and f n]. Parameters 1 to 4 are varied for hp n], and parameters 5 was varied for f n].

10

Table 3.1: Coordinates for excitation and listening points Position x (m) y (m) z (m) Excitation point 1 0.225 0.490 0.000 Excitation point 2 0.185 0.435 0.000 Listening point 1 0.210 0.070 0.805 Listening point 2 0.600 0.070 0.535 Parameter 1: Parameter 2: Parameter 3: Parameter 4: Parameter 5: Excitation points 1 and 2 Listening points 1 and 2 Right and left ears With and without head and torso Four rotation speeds of the motor (30,43, 38 and 50 Hz)

Directions of axes x; y; z for coordinates, and positions of parameters 1 and 2 are shown in Figure 3.3. We set the origin point of axes at the upper left corner of the plate. The exact coordinates for each position are given in Table 3.1. The coordinates of a listening point is the center between two ears, or between two microphones which imitates two ears. The position of parameter 3 was shown in Figure 3.4. The distance of two microphones are 15 cm. To distinguish which microphones of the two relates to thez 0 0.4 m x

b 0.6 m a a: Excitation point 1 b: Excitation point 2

y

Figure 3.3: Direction of axes and position of the excitation points: The plate is set invibration by a motor at an excitation point 1 or 2.

11

x Plate

Left ear z

Right ear

15 cm

Figure 3.4: Direction of the head and distance between the arti cial ears: The listening points are set facing the plate. The coordinates of listening points represents the center of the two ears. right or the left ear, a side of the head facing the plate is taken as the face of the head. The parameter 4 is varied only for measurement of pe n] using arti cial head and torso around microphones. Since hps n] with head and torso was not established, ps n] with them was not synthesized. Rotation speed given for parameter 5 was measured on the rst gear of the motor as the number of rotations per second (Hz) as shown in gure 3.5. Each rotation speed is de ned as follows. - Rotation speed 1: 30 Hz - Rotation speed 2: 43 Hz - Rotation speed 3: 38 Hz - Rotation speed 4: 50 Hz Those excitation forces by motor are introduced in Table 3.2. Their characteristics are also shown in time and frequency domain in Appendix C.

12

Rotation speed (Hz)

Figure 3.5: Rotation measurement: Rotation speed was de ned as the number of rotationsin one second at the rst gear of the motor. Four kinds of rotation speed were prepared as a parameter (30, 43, 38 and 50 Hz).

Table 3.2: Names of the les and their parameter condition: f n] and F k] correspond to

respectively force in the time domain and that in the frequency domain. Excitation points are shown in Figure 3.3. Rotation speeds are 1 (30 Hz), 2 (43 Hz), 3 (38 Hz), and 4 (50 Hz).

ftm11 ftm12 ftm13 ftm14 ftm21 ftm22 ftm23 ftm24

f n]

FTM11 FTM12 FTM13 FTM14 FTM21 FTM22 FTM23 FTM24

F k]

Excitation point Rotation speed 1 1 1 2 1 3 1 4 2 1 2 2 2 3 2 4

13

14

Chapter 4

Practical procedures4.1 Data style of the functionsForce f n] and sound pressure pe n] were measured in experiments at INSA de Lyon. Both of them were written in time domain as following: - Sampling frequency fs = 12800 Hz - Number of samples: 32768 - 2.56 seconds duration (corresponding to 0.39 Hz frequency resolution) Synthesized sound pressure ps n] was made to have same characteristics as pe n]. The transfer function Hps k] was calculated at INSA de Lyon. The data les, transmitted to ENST, corresponded to a half of the whole frequency range of the transfer function, since the functions are conjugate-symmetric as described before. The transmitted les have the data speci cations as following: - Maximum frequency fm = 5000 Hz - 12800 complex exponentials - Frequency resolution: 0.39 Hz (for detailed description, see Section 4.2.1). The data were reconstructed into the whole function Hps k] to have a structure shown below: - Sampling frequency fs = 12800 Hz - 32768 complex exponentials - Frequency resolution: 0.39 Hz This reconstruction procedure is described in Section 4.2.2. 15

Frequency 3.9062500e-01 7.8125000e-01 1.1718750e+00 5.0000000e+03

.. .

Abs. value 1.5937982e-06 6.3776744e-06 1.4359084e-05 2.0564840e-02

.. .

Re. part -1.5937717e-06 -6.3772502e-06 -1.4356935e-05 8.3818261e-03

.. .

Im. part 9.1911058e-09 7.3556195e-08 2.4840616e-07 -1.8779180e-02

.. .

Figure 4.1: Illustration of transmitted data le (pfcd101): The rst column shows the frequency (Hz). The third and the fourth column give the real and the imaginary part of the simulated transfer function.

A data le, which contains simulated transfer function Hps k], consists of 4 columns and 12800 rows. - The rst column: Frequency in Hz - The second column: Absolute value of the transfer function - The third column: Real part of the transfer function Re(Hps k]) - The fourth column: Imaginary part of the transfer function Im(Hps k]) The third column and the fourth column make complex exponentials;

4.2.1 Transmitted data le

4.2 Simulation model

Hps k] = Re(Hps k]) + jIm(Hps k]); 1 k 12800:The data le is illustrated in Figure 4.1.

(4.1)

4.2.2 Getting an impulse responseThe reconstruction of the transmitted transfer function was done by the following steps: 1. Computation of complex exponentials 2. Zero-padding 3. Patching the transfer value at 0 Hz 4. Symmetric addition of complex conjugates 5. Phase delay 16

The rst step is to realize the complex exponentials from real and imaginary part of the simulated transfer function Hps k], given in the data le (Figure 4.1). Those absolute values are shown in the rst plot of Figure 4.2. The second step is for a problem which appears in synthesis. Since originally fs = 10 kHz for the simulation, convolution (or superposition) of hps n] and f n](fs = 12:8 kHz) is impossible: There is no proper sampling frequency for listening. To solve this problem, zeros were added at the end of sequence, which corresponds to the region from 5 kHz to 6.4 kHz (see Figure 4.2, the second plot). Thus we obtain Hps k] with fn = 6:4 kHz. The third step is to patch the value of transfer rate at 0 Hz. It is necessary for the IDFT operation; the DFT is designed from 0 Hz (see Section 2.1). The absolute value at 0.39 Hz was patched at the beginning of the sequence.

Simulated frequency response (pfcd1011) 2 Amplitude (Pa/N) 1.5 1 0.5 0 0 2 Amplitude (Pa/N) 1.5 1 0.5 0 0 2 Amplitude (Pa/N) 1.5 1 0.5 0 0 2000 4000 6000 8000 Step4 frequency (Hz) 10000 12000 2000 4000 6000 8000 Step3 frequency (Hz) 10000 12000 2000 4000 6000 8000 Step1 frequency (Hz) 10000 12000

Figure 4.2: Reconstruction of transfer function: The top gure presents the absolute value of complex exponentials. Frequency region is limited to 5 kHz. The middle gure shows the addition of zeros from 5 kHz to 6.4 kHz in order to change the sampling frequency to 12.8 kHz from 10 kHz. The bottom gure shows the result of symmetric addition of complex conjugations. 17

The fourth step is reconstruction of the other half part of Hps k] (symmetry property, presented by Eq. 2.6). Thus it works as the complete DFT of hps n] for N = 32768. This is illustrated in the third plot in Figure 4.2. The fth step is for another problem which appeared after IDFT; We had unexpected increase of amplitude at the end of hps n]. We consider the reason as a periodicity error in the discrete time system and eliminated it using phase delay. 128 samples at the end of hps n] was shifted to its beginning by phase delay following Eq. 2.5. That is,128k hps n 128] () WN Hps k]; N = 32768:

(4.2)

This phenomenon and the e ect of phase delay are shown in Figure 4.3.Impulse response with and without phase delay (pfcd101) 0.02 Amplitude (Pa/N) 0.01 0 0.01 0.02

0 x 103

0.5

1

1.5 Time (s) (without phase delay)

2

2.5

3

1 Amplitude (Pa/N) 0.5 0 0.5

1 2.4 0.02 Amplitude (Pa/N) 0.01 0 0.01 0.02

2.42

2.44

2.46

2.48 2.5 2.52 Time 2.42.6 (s) (without phase delay)

2.54

2.56

2.58

2.6

0

0.5

1

1.5 Time (s) (with phase delay)

2

2.5

3

0.02 Amplitude (Pa/N) 0.01 0 0.01 0.02

0

0.02

0.04

0.06

0.08 0.1 0.12 Time 00.2 (s) (with phase delay)

0.14

0.16

0.18

0.2

Figure 4.3: E ect of phase delay: Without a phase delay (top), there is an increase of amplitude at the end of the impulse response which is visible at the upper-middle plot. This region was shifted to the beginning of the sequence (bottom). The entire impulse response after phase delay is also shown (lower-middle). Finally, we computed IDFT on this reconstructed Hps k]. We obtained hps n] having 2.56 s duration and 12.8 kHz sampling frequency. 18

4.2.3 SynthesisThe simulated impulse response hps n] was linearly convolved with force f n] to obtain the synthesized sound pressure ps n] (see Eq. 3.3). Actual computation was done by ltering using overlap-add method (see Section 2.4). Examples of hps n]; f n] and ps n] are shown in Figure 4.4.0.02 Amplitude (Pa/N) 0.01 0 0.01 0.4 Force (N) 0.2 0 0.2 0.4 0.02 0.01 0 0.01 0.02 0 0.5 1 1.5 ps[n] (pcd1011) time (s) 2 2.5 3 0 0.5 1 1.5 f[n] (ftm11) time (s) 2 2.5 3

0

0.5

1

1.5 hps[n] (cird101) time (s)

2

2.5

3

convolution product of the theoretically derived impulse response (top) and the measured force (middle).

Figure 4.4: Synthesis by linear convolution: The simulated sound pressure (bottom) is the

4.3 Experiment4.3.1 Transmitted data leThe results of measurements for both f n] (force) and pe n] (sound pressure) were sent as data les having the same style. A le contains two columns and 32768 rows as shown in Figure 4.5. - The rst column: time in second - The second column: force f n] (N), or ps n] (Pa) 19

Sound pressure (Pa)

t 7.8125000e-005 1.5625000e-004 2.3437500e-004 2.5600000e+000

.. .

f n] 1.1564700e-002 1.5534670e-002 2.1317020e-002 2.5600000e+000

.. .

Figure 4.5: Illustration of transmitted data le (ftm11): The left column shows time insecond, and the right column shows force (N).

As discussed in Section 4.2.2, the maximum frequency fm was 5 kHz in simulation, while the Nyquist frequency fN was adjusted to 6.4 kHz. The di erence of spectrum between Pe n] (in experiment) and Ps n] (by synthesis), which was caused by this, is shown in Figure 4.6. To obtain the same spectral rage as ps n], pe n] was ltered by a FIR low-pass lter hf n], designed by Kaiser window method (see Section 2.5). hf n] has the 400th order, stopband from 5 kHz to 6.4 kHz, and 60dB sidelobe amplitude (M = 401; = 5:65). Its frequency response is given in Figure 4.7. Figure 4.8 presents the result of ltering for Pe n].40 20 Magnitude (dB) 0 20 40 60 80 0 1000 2000 3000 4000 5000 Unfiltered Pe[k] (PTMD1011) frequency (Hz) 6000 7000

4.3.2 Filtering experimental sound pressure

40 20 Magnitude (dB) 0 20 40 60 80 0 1000 2000 3000 4000 5000 Ps[k] (PCD1011) frequency (Hz) 6000 7000

Figure 4.6: Comparison of spectra between the measured sound pressure (top) and the synthesized sound pressure (bottom): The truncation of the synthesized sound is caused by the maximum frequency limitation in simulation. 20

20 0 20 Magnitude (dB) 40 60 80 100 120 140 160 0 1000 2000 3000 4000 Frequency (Hz) 5000 6000 7000

Figure 4.7: Frequency response of the lter hf n]: It is used for ltering of measured sound pressure to cut the frequency region from 5 kHz to 6.4 kHz.

40 20 Magnitude (dB) 0 20 40 60 80 0 1000 2000 3000 4000 5000 Filtered Pe[k] (PTMD1011) frequency (Hz) 6000 7000

40 20 Magnitude (dB) 0 20 40 60 80 0 1000 2000 3000 4000 5000 Ps[k] (PCD1011) frequency (Hz) 6000 7000

Figure 4.8: Spectrum of resulted sound pressures: The measured sound pressure afterltering (top) and the synthesized sound pressure (bottom)

21

22

Chapter 5

Preparation for psychoacoustical tests5.1 Listening tests and required stimuliFor psychoacoustical analysis, Three kinds of listening tests were prepared; 1. Dissimilarity test 2. Matching test 3. Discrimination test Dissimilarity test is to know the perceptive structure of the sounds. We prepared the measured sounds and the simulated sounds for the left ear, without dummy head, and variation of the other parameters, i.e. excitation points (1 and 2), listening points (1 and 2), and rotation speeds (1, 2, 3, and 4). The test has two parts: One part consists of 16 measured sound pressures. The other part consisted of 16 simulated sound pressures. In each part, all the possible combination of two sounds from the 16 sounds are presented to a listener in random order. The listener is required to judge how the two sound are di erent, using a scale which shows very similar at one side and very di erent at the other side. Matching test is to let the listeners make pairs of sounds from two groups of sounds. They are presented two groups of sounds, and required to chose one sound from each of two groups, which sound similar to each other. It uses 32 stimuli which are also used in dissimilarity test. The measured 16 sounds forms a group, and the synthesized 16 sounds forms the other group. Discrimination test was done between the experimental sounds recorded with dummy head and the experimental sounds recorded without dummy head. While monoral sounds of left ear channel were used for the other tests, stereo sounds recorded by right and left ear channels were used for the discrimination test. We prepared 16 variation of the other parameters: Excitation points (1 and 2), listening points (1 and 2), and rotation speeds (1, 2, 3, and 4). Thus we obtained 16 pairs of 23

the sounds recorded with and without dummy head. The listeners are presented four possible combination for one pair (e.g. aa, ab, ba, bb), and required to categorize the two sounds as either same or di erent .

5.2 Sound les

The stimuli for the psychoacoustical tests are contained in sound les with PCM Raw Data format having extension .snd . This format consists of sample sequence of integer number in 16 bits resolution as following: 1. Search the maximum value of the sound pressure 2. Division of the sequence by the maximum value (normalization) 3. Multiplication by 32767 (to have the possible level 216 1) 4. Rounding the fractional numbers (data style double) to the integer numbers Sudden decrease of sound pressure at the end gives an impression like a pulse sound. To eliminate this e ect, the sound les were triangular windowed at the end of the signal for 50 ms (640 samples). This windowing is shown in Figure 5.1.Normalized sound pressure 4 2 0 2 4 2.4 x 104

5.2.1 Format of sound le

5.2.2 Windowing of the sounds

x 10

4

2.42

2.44

2.46 2.48 2.5 2.52 time (s) without windowing (pcd1011)

2.54

2.56

Normalized sound pressure

4 2 0 2

4 2.4

2.42

2.44

2.46 2.48 2.5 time (s) with windowing (pcd1011)

2.52

2.54

2.56

Figure 5.1: The sound without windowing (top) and the sound after windowing (bottom): The triangular window was used for at the end of 50 ms (640 samples). These sound les are sent to IRCAM and are going to be examined in psychoacoustical tests organized there. 24

ConclusionSummary of obtained signalsWe got 32 synthesized and 32 measured sounds, without the dummy head, in variation of excitation points (1,2), listening points (1,2), ears (right and left), and rotation speed of the motor (1,2,3,4). Moreover 32 sounds were recorded in the same condition of parameters but with dummy head. The names of the les for all the signals are listed in Appendix B. Their waveforms and spectra are presented in Appendix C. Since the force and the sound pressure were not measured at the same time in experiments, we couldn't calculate experimental impulse response and transfer function (Section 3.2). The comparison between measured and simulated transfer functions, therefore, was not done. In spite of this, comparison in terms of sound pressure is possible though it is strongly a ected by random variations of motor force.

Comments on spectra of the signalsThe spectra of motor force have a high magnitude only in lower frequencies. Figures C.1 to C.4 in Appendix C show the number of peaks with a high magnitude is not many. The motor generates particularly strong force in limited frequencies from 0 to 400 Hz, which mainly a ect the vibration of the plate. Simulated impulse responses show that the parameter right and left ear doesn't a ect the transfer function noticeably in their spectra (Figures C.5 to C.8). It gives only little di erences in lower frequency region (0 to 700 Hz), and slightly greater di erences in higher frequency region (up from 700 Hz). Also the parameter of excitation point does not a ect the transfer function at all. Simulation of transfer function have exactly same complex value under the variation of excitation point. If the synthesized sounds have any di erence by this parameter (excitation point), it is caused by the force signal but not by the simulated impulse response. In comparison of the synthesized and recorded sounds (Figures C.9 to C.40), the whole spectra are roughly similar to each other. Especially in the region from 0 to 25

400 Hz, they look quite similar in the forms. In the region up from 400 Hz, several peaks exist in spectra of synthesized sounds, while those peaks are not found in spectra of recorded sounds. More important point is, the synthesized sounds, in comparison with the recorded one, are characterized by the presence of strong peaks and dips (Figure 5.2). This suggests that the damping coe cient of simulation was somewhat underestimated.Recorded sound (ptmd2012) 40 30 20 Magnitude(dB) Magnitude(dB) 10 0 10 20 30 40 50 0 200 400 600 Frequency 01000(Hz) 800 1000 60 0 200 400 600 Frequency 01000(Hz) 800 1000 20 40 Synthesized sound (pcd2012)

0

20

40

Figure 5.2: Simulated sound spectrum (right) has sharper peaks than recorded sound spectrum (left) though rough forms look similar. This implies the damping coe cient was underestimated. In comparison of the experimental sounds with and without dummy head (between Figures C.41 to C.56 and the left columns of Figures C.9 to C.40), the parameter of dummy head does not give so much di erence in frequency domain. The parameter increases the magnitude slightly in the region from 500 to 1000 Hz when recorded with dummy head. Right and left ear sound pressure recorded with dummy head shows a little the e ect of the dummy head (Figure C.41 to C.56). With excitation point 1, the magnitude of right ear increase in the region from 2000 to 3000 Hz. With excitation point 2, the magnitude of the right ear decrease in the region from 2000 to 3000 Hz. Any way these di erences are very slight.

26

Bibliography1] Oppenheim, A. V., and Schafer, R. W., Discrete-Time Signal Processing, Prentice-Hall, Englewood Cli s, NJ, 1989. 2] Oppenheim, A. V., and Schafer, R. W., Digital Signal Processing, Prentice-Hall, Englewood Cli s, NJ, 1975.

27

28

Appendix A

Program listIn this chapter, the M- les used in the procedures are presented.function % % % % % % % s,irep]=reconst(filename);

s,irep]=reconst('file') computes reconstruction of a data file of simulated frequency response sent from LVA INSA de Lyon. The data file has 5kHz Nyquist frequency. This function adds zeros till Nyquist frequency 6.4kHz. Resulted frequency response has fs=12.8kHz, df=1/2.56 Hz, number of samples 32768. This function also returns simulated impulse response whose time duration is 2.56 seconds.

%number of samples n=12800*2; %number of samples after zero-padding np=32768; %sampling frequency after the zero-padding fs=12800; s=load(filename); s=s(:,3)+i*s(:,4); % zero-padding s= s; zeros(np/2-length(s),1)]; % addition 0 Hz s= abs(s(1)); s]; % addition of symmetric comjugation

29

s= s; conj(fliplr(s(2:np/2)')')]; % phase delay w=2*pi*(1:np)/(np); h=exp(j*w*128); se=s.*h'; %impulse response irep=real(ifft(se)); irep_snd=nor(irep); ---------function p,ps]=syn(k,l);

% p,ps]=syn(k,l) returns linear convolution of sequences % k and l, and its normalized integer sequence (resolution 16 % bits) to export as a sound file. p=fftfilt(k,l); ps=nor(p); ---------function pression,n]=filpe(pression);

% pression,n]=filpe(pression) returns low-pass filtered sound % pressure and its normalized integer sequence for a sound file. %filter design A=60; beta=0.1102*(A-8.7); M=400;

% sidelobe amplitude % shape parameter beta % order of this FIR filter

lpf=fir1(M,5000/6400,kaiser(M+1,beta)); %filtering pression=filter(lpf,1,pression); n=nor(pression); ---------function s,s_db]=freqrepdb(pression,ns);

30

% s,s_db]=freqrepdb(pression,ns) returns frequency response % of a sound pressure sequence with length ns, also returns dB value % of frequency response.

% computation of frequency response s=fft(pression); % dB value s_db=20*log10(abs(s(1:ns/2))); ---------function n=nor(file); % n=nor(file) returns an integer and normalized sound data % possible level is 32768*2=2^16 (16 bits resolution) % ATTENTION: the resulted data is ROUNDED

fm=max(abs(file)); fn=file/fm; n=round(fn.*32767);

31

32

Appendix B

Index of signalsSimulation and synthesisWe got eight simulated impulse response hps n]. As their convolution products with eight forces, we got 32 synthesized sound pressures (ps n]). The impulse responses and the synthesized sounds are listed in following Tables B.1 and B.2.

Measured sound pressuresFiles of the sound pressures pe n], recorded in experiments are listed in Tables B.3 and B.4 with their names and the parameter conditions. We got 64 varieties of parameters. Table B.1: Files for simulated impulse responses of the plate: pfc is for simulated transfer function. d is for right ear, g is for left ear. Parameters are varied for right and left ear, excitation point 1 (centered) and 2 (sided), without dummy head, listening point 1 (centered) and 2 (sided). cird101 cird102 cird201 cird202 cirg101 cirg102 cirg201 cirg202

hps n]

pfcd101 pfcd102 pfcd201 pfcd202 pfcg101 pfcg102 pfcg201 pfcg202

Hps k]

Ear Excitation Head Listening right 1 0 1 right 1 0 2 right 2 0 1 right 2 0 2 left 1 0 1 left 1 0 2 left 2 0 1 left 2 0 2

33

Table B.2: Files of synthesized sound pressures: d is for right ear, g is for left ear. Parameters are varied for right and left ear, excitation point 1 (centered) and 2 (sided), without dummy head, rotation speed of motor 1, 2, 3, 4 (30 Hz, 43 Hz, 38 Hz and 50 Hz), listening point 1 (centered) and 2 (sided). pcd1011 pcd1012 pcd1021 pcd1022 pcd1031 pcd1032 pcd1041 pcd1042 pcd2011 pcd2012 pcd2021 pcd2022 pcd2031 pcd2032 pcd2041 pcd2042 pcg1011 pcg1012 pcg1021 pcg1022 pcg1031 pcg1032 pcg1041 pcg1042 pcg2011 pcg2012 pcg2021 pcg2022 pcg2031 pcg2032 pcg2041 pcg2042

ps n]

Convolution pair cird101*ftm11 cird102*ftm11 cird101*ftm12 cird102*ftm12 cird101*ftm13 cird102*ftm13 cird101*ftm14 cird102*ftm14 cird201*ftm21 cird202*ftm21 cird201*ftm22 cird202*ftm22 cird201*ftm23 cird202*ftm23 cird201*ftm24 cird202*ftm24 cirg101*ftm11 cirg102*ftm11 cirg101*ftm12 cirg102*ftm11 cirg101*ftm13 cirg102*ftm13 cirg101*ftm14 cirg102*ftm14 cirg201*ftm21 cirg202*ftm21 cirg201*ftm22 cirg202*ftm22 cirg201*ftm23 cirg202*ftm23 cirg201*ftm24 cirg202*ftm24

Ear Excitation Head Rotation Listening right 1 0 1 1 right 1 0 1 2 right 1 0 2 1 right 1 0 2 2 right 1 0 3 1 right 1 0 3 2 right 1 0 4 1 right 1 0 4 2 right 2 0 1 1 right 2 0 1 2 right 2 0 2 1 right 2 0 2 2 right 2 0 3 1 right 2 0 3 2 right 2 0 4 1 right 2 0 4 2 left 1 0 1 1 left 1 0 1 2 left 1 0 2 1 left 1 0 2 2 left 1 0 3 1 left 1 0 3 2 left 1 0 4 1 left 1 0 4 2 left 2 0 1 1 left 2 0 1 2 left 2 0 2 1 left 2 0 2 2 left 2 0 3 1 left 2 0 3 2 left 2 0 4 1 left 2 0 4 2

34

Table B.3: Files of experimental sound pressures (right ear): Parameters are varied for right and left ear, excitation point 1 (centered) and 2 (sided), without dummy head, rotation speed of motor 1, 2, 3, 4 (30 Hz, 43 Hz, 38 Hz and 50 Hz), listening point 1 (centered) and 2 (sided). ptmd1011 ptmd1012 ptmd1021 ptmd1022 ptmd1031 ptmd1032 ptmd1041 ptmd1042 ptmd1111 ptmd1112 ptmd1121 ptmd1122 ptmd1131 ptmd1132 ptmd1141 ptmd1142 ptmd2011 ptmd2012 ptmd2021 ptmd2022 ptmd2031 ptmd2032 ptmd2041 ptmd2042 ptmd2111 ptmd2112 ptmd2121 ptmd2122 ptmd2131 ptmd2132 ptmd2141 ptmd2142

pe n]

Ear Excitation Head Rotation Listening right 1 0 1 1 right 1 0 1 2 right 1 0 2 1 right 1 0 2 2 right 1 0 3 1 right 1 0 3 2 right 1 0 4 1 right 1 0 4 2 right 1 1 1 1 right 1 1 1 2 right 1 1 2 1 right 1 1 2 2 right 1 1 3 1 right 1 1 3 2 right 1 1 4 1 right 1 1 4 2 right 2 0 1 1 right 2 0 1 2 right 2 0 2 1 right 2 0 2 2 right 2 0 3 1 right 2 0 3 2 right 2 0 4 1 right 2 0 4 2 right 2 1 1 1 right 2 1 1 2 right 2 1 2 1 right 2 1 2 2 right 2 1 3 1 right 2 1 3 2 right 2 1 4 1 right 2 1 4 2

35

Table B.4: Files of experimental sound pressures (left ear): Parameters are varied for right and left ear, excitation point 1 (centered) and 2 (sided), without dummy head, rotation speed of motor 1, 2, 3, 4 (30 Hz, 43 Hz, 38 Hz and 50 Hz), listening point 1 (centered) and 2 (sided). ptmg1011 ptmg1012 ptmg1021 ptmg1022 ptmg1031 ptmg1032 ptmg1041 ptmg1042 ptmg1111 ptmg1112 ptmg1121 ptmg1122 ptmg1131 ptmg1132 ptmg1141 ptmg1142 ptmg2011 ptmg2012 ptmg2021 ptmg2022 ptmg2031 ptmg2032 ptmg2041 ptmg2042 ptmg2111 ptmg2112 ptmg2121 ptmg2122 ptmg2131 ptmg2132 ptmg2141 ptmg2142

pe n]

Ear Excitation Head Rotation Listening left 1 0 1 1 left 1 0 1 2 left 1 0 2 1 left 1 0 2 2 left 1 0 3 1 left 1 0 3 2 left 1 0 4 1 left 1 0 4 2 left 1 1 1 1 left 1 1 1 2 left 1 1 2 1 left 1 1 2 2 left 1 1 3 1 left 1 1 3 2 left 1 1 4 1 left 1 1 4 2 left 2 0 1 1 left 2 0 1 2 left 2 0 2 1 left 2 0 2 2 left 2 0 3 1 left 2 0 3 2 left 2 0 4 1 left 2 0 4 2 left 2 1 1 1 left 2 1 1 2 left 2 1 2 1 left 2 1 2 2 left 2 1 3 1 left 2 1 3 2 left 2 1 4 1 left 2 1 4 2

36

Appendix C

Waveforms and spectra of signalsFigures from C.1 to C.4 presents the analysis of the force signals. Figures from C.5 to C.8 presents analysis of the simulated impulse response. Figures from C.9 to C.40 presents comparison of simulated and measured sound pressures. Figures from C.41 to C.56 presents comparison between left and right ear channel for the experimental sounds recorded with dummy head.

37

Force ( ftm11 ) 0.4 0.2 Force (N) 0 0.2 0.4 0 100 50 0 50 100 1 time (s) 100 50 0 50 100 2 3 Force (N) 0.4 0.2 0 0.2 0.4 0

Force ( ftm12 )

1 time (s)

2

3

Magnitude(dB)

0

2000 4000 6000 Frequency (Hz)

Magnitude(dB)

0

2000 4000 6000 Frequency (Hz)

80 60 Magnitude(dB) 40 20 0 20 40 0 500 Frequency 01000(Hz) 1000 Magnitude(dB)

80 60 40 20 0 20 40 0 500 Frequency 01000(Hz) 1000

Figure C.1: Forces (1): Waveforms and spectra of the force at excitation point 1 (centered).Left column: Rotation speed 1 (30 Hz). Right column: Rotation speed 2(43 Hz)

38


Force ( ftm14 )

1 time (s)

2

3

Magnitude(dB)

0

2000 4000 6000 Frequency (Hz)

Magnitude(dB)

0

2000 4000 6000 Frequency (Hz)


80 60 40 20 0 20 40 0 500 Frequency 01000(Hz) 1000

Figure C.2: Forces (2): Waveforms and spectra of the force at excitation point 1 (centered).Left column: Rotation speed 3 (38 Hz). Right column: Rotation speed 4(50 Hz)

39


Force ( ftm22 )

1 time (s)

2

3

Magnitude(dB)

0

2000 4000 6000 Frequency (Hz)

Magnitude(dB)

0

2000 4000 6000 Frequency (Hz)


80 60 40 20 0 20 40 0 500 Frequency 01000(Hz) 1000

Figure C.3: Forces (3): Waveforms and spectra of the force at excitation point 2 (sided).Left column: Rotation speed 1 (30 Hz). Right column: Rotation speed 2(43 Hz)

40


Force ( ftm24 )

1 time (s)

2

3

Magnitude(dB)

0

2000 4000 6000 Frequency (Hz)

Magnitude(dB)

0

2000 4000 6000 Frequency (Hz)


80 60 40 20 0 20 40 0 500 Frequency 01000(Hz) 1000

Figure C.4: Forces (4): Waveforms and spectra of the force at excitation point 2 (sided).Left column: Rotation speed 3 (38 Hz). Right column: Rotation speed 4(50 Hz)

41

Simulated impulse response ( cirg101 ) 0.02 0.01 Force (N) 0 0.01 0.02 Force (N) 0 1 time (s) 50 0 50 100 150 2 3

Simulated impulse response ( cird101 ) 0.02 0.01 0 0.01 0.02

0

1 time (s)

2

3

50 0 50 100 150

Magnitude(dB)

0

1000 2000 3000 4000 5000 Frequency (Hz)

Magnitude(dB)

0

1000 2000 3000 4000 5000 Frequency (Hz)

50 0 50 100 150

50 0 50 100 150

Magnitude(dB)

0

500 Frequency 01000(Hz)

1000

Magnitude(dB)

0


1000

Figure C.5: Simulated impulse response (1): Waveforms and spectra of the simulated impulse response in the condition: Excitation point 1 (centered), without dummy head, listening point 1 (centered). Left column: Left ear. Right column: Right ear.

42



0

1 time (s)

2

3

50 0 50 100 150

Magnitude(dB)

0

1000 2000 3000 4000 5000 Frequency (Hz)

Magnitude(dB)

0

1000 2000 3000 4000 5000 Frequency (Hz)

50 0 50 100 150

50 0 50 100 150

Magnitude(dB)

0


1000

Magnitude(dB)

0


1000

Figure C.6: Simulated impulse response (2): Waveforms and spectra of the simulated impulse response in the condition: Excitation point 1 (centered), without dummy head, listening point 2 (sided). Left column: Left ear. Right column: Right ear.

43



0

1 time (s)

2

3

50 0 50 100 150

Magnitude(dB)

0

1000 2000 3000 4000 5000 Frequency (Hz)

Magnitude(dB)

0

1000 2000 3000 4000 5000 Frequency (Hz)

50 0 50 100 150

50 0 50 100 150

Magnitude(dB)

0


1000

Magnitude(dB)

0


1000

Figure C.7: Simulated impulse response (3): Waveforms and spectra of the simulated impulse response in the condition: Excitation point 2 (sided), without dummy head, listening point 1 (centered). Left column: Left ear. Right column: Right ear.

44



0

1 time (s)

2

3

50 0 50 100 150

Magnitude(dB)

0

1000 2000 3000 4000 5000 Frequency (Hz)

Magnitude(dB)

0

1000 2000 3000 4000 5000 Frequency (Hz)

50 0 50 100 150

50 0 50 100 150

Magnitude(dB)

0


1000

Magnitude(dB)

0


1000

Figure C.8: Simulated impulse response (4): Waveforms and spectra of the simulated impulse response in the condition: Excitation point 2 (sided), without dummy head, listening point 2 (sided). Left column: Left ear. Right column: Right ear.

45

Measured sound (ptmd1011) 0.1 Sound pressure(Pa) 0.05 0 0.05 0.1 Sound pressure(Pa) 0.05

Simulated sound (pcd1011)

0

0

1 time (s)

2

3

0.05

0

1 time (s)

2

3

50 Magnitude(dB) Magnitude(dB) 0 2000 4000 6000 Frequency (Hz)

50

0

0

50

50

100

100

0

2000 4000 6000 Frequency (Hz)

60 40 Magnitude(dB) 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000 Magnitude(dB)

60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000

sound pressure in the condition: Right ear, excitation point 1 (centered), without dummy head, rotation speed 1 (30 Hz), listening point 1 (centered). Left column: Experimental sound. Right column: Synthesized sound.

Figure C.9: Comparison between pcd1011 and ptmd1011: Waveforms and spectra of the

46



0

0

1 time (s)

2

3

0.05

0

1 time (s)

2

3


50

0

0

50

50

100

100

0

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60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000

Figure C.10: Comparison between pcd1012 and ptmd1012: Waveforms and spectra of the sound pressure in the condition: Right ear, excitation point 1 (centered), without dummy head, rotation speed 1 (30 Hz), listening point 2 (sided). Left column: Experimental sound. Right column: Synthesized sound.

47



0

0

1 time (s)

2

3

0.05

0

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2

3


50

0

0

50

50

100

100

0

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60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000

Figure C.11: Comparison between pcd1021 and ptmd1021: Waveforms and spectra of the sound pressure in the condition: Right ear, excitation point 1 (centered), without dummy head, rotation speed 2 (43 Hz), listening point 1 (centered). Left column: Experimental sound. Right column: Synthesized sound.

48



0

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2

3

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49



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51



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52



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53



0

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3

0.05

0

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2

3


50

0

0

50

50

100

100

0

2000 4000 6000 Frequency (Hz)


60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000

Figure C.17: Comparison between pcd2011 and ptmd2011: Waveforms and spectra of the sound pressure in the condition: Right ear, excitation point 2 (sided), without dummy head, rotation speed 1 (30 Hz), listening point 1 (centered). Left column: Experimental sound. Right column: Synthesized sound.

54



0

0

1 time (s)

2

3

0.05

0

1 time (s)

2

3


50

0

0

50

50

100

100

0

2000 4000 6000 Frequency (Hz)


60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000

Figure C.18: Comparison between pcd2012 and ptmd2012: Waveforms and spectra of the sound pressure in the condition: Right ear, excitation point 2 (sided), without dummy head, rotation speed 1 (30 Hz), listening point 2 (sided). Left column: Experimental sound. Right column: Synthesized sound.

55



0

0

1 time (s)

2

3

0.05

0

1 time (s)

2

3


50

0

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60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000


56



0

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3

0.05

0

1 time (s)

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3


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57



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3

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0

1 time (s)

2

3


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60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000


58



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3


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59



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60



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61

Measured sound (ptmg1011) 0.1 Sound pressure(Pa) 0.05 0 0.05 0.1 Sound pressure(Pa) 0.05

Simulated sound (pcg1011)

0

0

1 time (s)

2

3

0.05

0

1 time (s)

2

3


50

0

0

50

50

100

100

0

2000 4000 6000 Frequency (Hz)


60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000

sound pressure in the condition: Left ear, excitation point 1 (centered), without dummy head, rotation speed 1 (30 Hz), listening point 1 (centered). Left column: Experimental sound. Right column: Synthesized sound.

Figure C.25: Comparison between pcg1011 and ptmg1011: Waveforms and spectra of the

62



0

0

1 time (s)

2

3

0.05

0

1 time (s)

2

3


50

0

0

50

50

100

100

0

2000 4000 6000 Frequency (Hz)


60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000


sound pressure in the condition: Left ear, excitation point 1 (centered), without dummy head, rotation speed 1 (30 Hz), listening point 2 (sided). Left column: Experimental sound. Right column: Synthesized sound.

63



0

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2

3

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0

1 time (s)

2

3


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60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000



64



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65



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66



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67



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68



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69



0

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1 time (s)

2

3

0.05

0

1 time (s)

2

3


50

0

0

50

50

100

100

0

2000 4000 6000 Frequency (Hz)


60 40 20 0 20 40 60 80 0 500 Frequency 01000(Hz) 1000


sound pressure in the condition: Left ear, excitation point 2 (sided), without dummy head, rotation speed 1 (30 Hz), listening point 1 (centered). Left column: Experimental sound. Right column: Synthesized sound.

70



0

0

1 time (s)

2

3

0.05

0

1 time (s)

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sound pressure in the condition: Left ear, excitation point 2 (sided), without dummy head, rotation speed 1 (30 Hz), listening point 2 (sided). Left column: Experimental sound. Right column: Synthesized sound.

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Measured sound (ptmg1111) 0.1 Sound pressure(Pa) 0.05 0 0.05 0.1 Sound pressure(Pa) 0.1 0.05 0 0.05 0.1

Measured sound (ptmd1111)

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Figure C.41: Comparison between ptmg1111 and ptmd1111: Waveforms and spectra of the experimental sound pressure in the condition: Excitation point 1 (centered), with dummy head, rotation speed 1 (30 Hz), listening point 1 (centered). Left column: Left ear. Right column: Right ear.

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Figure C.42: Comparison between ptmg1112 and ptmd1112: Waveforms and spectra of the

experimental sound pressure in the condition: Excitation point 1 (centered), with dummy head, rotation speed 1 (30 Hz), listening point 2 (sided). Left column: Left ear. Right column: Right ear.

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the experimental sound pressure recorded in the condition: Excitation point 1 (centered), with dummy head, rotation speed 2 (43 Hz), listening point 2 (sided). Left column: Left ear. Right column: Right ear.

Figure C.44: Comparison between ptmg1122 and ptmd1122: Waveforms and spectra of

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the experimental sound pressure in the condition: Excitation point 2 (sided), with dummy head, rotation speed 1 (30 Hz), listening point 1 (centered). Left column: Left ear. Right column: Right ear.


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the experimental sound pressure in the condition: Excitation point 2 (sided), with dummy head, rotation speed 1 (30 Hz), listening point 2 (sided). Left column: Left ear. Right column: Right ear.


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Documents

PhD.Thesis:Prediction of sound radiation from structures to assess percpective