Basic Acoustics + DSP

8/11/2019 Basic Acoustics + DSP

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Basic Acoustics +

Digital Signal Processing

January 14, 2014


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Just so you know...

Some ideas for finding consultants:

Kijiji and couch surfing

For today:

Part 1: Go through a review of the basics of (analog)acoustics.

Part 2: Converting sound from analog to digital format.

Any questions so far?


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Part 1: An Acoustic Dichotomy

Acoustically speaking, there are two basic kinds ofsounds:

1. Periodic

= an acoustic pattern which repeats, over time

The period is the length of time it takes for the

pattern to repeat

Periodic speech sounds = voiced segments + trills

2. Aperiodic Continuous acoustic energy which does not exhibit

a repeating pattern

Aperiodic speech sounds = fricatives


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The Third Wheel

There are also acoustic transients.

= aperiodic speech sounds which are not continuous

i.e., they are usually very brief

Transient speech sounds:

stop release bursts

clicks also (potentially) individual pulses in a trill

Lets look at the acoustic properties of each type of sound

in turn


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What does sound look like?

Air consists of floating air molecules

Normally, the molecules are suspended and evenly

spaced apart from each other

What happens when we push on one molecule?


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The force knocks that molecule against its neighbor

The neighbor, in turn, gets knocked against its neighbor

The first molecule bounces backpast its initial rest position

initial rest position


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The initial force gets transferred on down the line

rest

position #1

rest

position #2

The first two molecules swing back to meet up with each

other again, in between their initial rest positions

Think: bucket brigade


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Compression Wave

A wave of force travels down the line of molecules Ultimately: individual molecules vibrate back and forth,

around an equilibrium point

The transfer of force sets up what is called a

compression wave.

What gets compressed is the space between molecules

Check out what happens when we blow something up!


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Compression Wave

area of high pressure

(compression)

area of low pressure

(rarefaction)

Compression waves consist of alternating areas of

high and low pressure


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Pressure Level Meters Microphones

Have diaphragms, which move back and forth with air

pressure variations

Pressure variations are converted into electricalvoltage

Ears

Eardrums move back and forth with pressure variations

Amplified by components of middle ear

Eventually converted into neurochemical signals

We experience fluctuations in air pressure as sound


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Measuring Sound What if we set up a pressure level meter at one point in the

wave?

Time

pressure level meter


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Sine Waves

The reading on the pressure level meter will fluctuate

between high and low pressure values

In the simplest case, the variations in pressure level will

look like a sine wave.

time

pressure


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Other Basic Sinewave concepts Sinewaves are periodic; i.e., they recur over time.

The periodis the amount of time it takes for the pattern

to repeat itself.

A cycleis one repetition of the acoustic pattern. The frequencyis the number of times, within a given

timeframe, that the pattern repeats itself.

Frequency = 1 / period

usually measured in cycles per second, or Hertz

The peakamplitudeis the the maximum amount of

vertical displacement in the wave

= maximum (or minimum) amount of pressure


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Waveforms

A waveformplots air pressure on the y axis against time onthe x axis.


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Phase Shift

Even if two sinewaves have the same period andamplitude, they may differ in phase.

Phase essentially describes where in the sinewave cycle

the wave begins.

This doesnt affect the way that we hear the waveform.

Check out: sine waves vs. cosine waves!


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Complex Waves It is possible to combine more than one sinewave together

into a complex wave.

At any given time, each wave will have some amplitude

value.

A1(t1) := Amplitude value of sinewave 1 at time 1

A2(t1) := Amplitude value of sinewave 2 at time 1

The amplitude value of the complex wave is the sum ofthese values.

Ac(t1) = A1 (t1) + A2 (t1)


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Complex Wave Example Take waveform 1:

high amplitude

low frequency

Add waveform 2:

low amplitude

high frequency

The sum is this

complex waveform:

+

=


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A Real-Life Example 480 Hz tone

620 Hz tone

the combo = ?


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Spectra One way to represent complex waves is with waveforms:

y-axis: air pressure

x-axis: time

Another way to represent a complex wave is with a power

spectrum(or spectrum, for short).

Remember, each sinewave has two parameters:

amplitude

frequency

A power spectrum shows:

amplitude on the y-axis

frequency on the x-axis


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One Way to Look At It

Combining 100 Hz and 1000 Hz sinewaves results in

the following complex waveform:

a

m

pl

i

tu

de

time


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The Third Way

A spectrogramshows how the spectrum of a complexsound changes over time.

f

r

eq

u

e

n

cy

time

intensity (related to amplitude) is represented by

shading in the z-dimension.

1000 Hz

100 Hz


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Fundamental Frequency

One last point about periodic sounds:

Every complex wave has a fundamental frequency(F0).

= the frequency at which the complex wave pattern

repeats itself.

This frequency happens to be the greatest common

denominator of the frequencies of the component waves.

Example: greatest common denominator of 100 and

1000 is 100.

GCD of 480 and 620 Hz is 20.

GCD of 600 and 800 Hz is 200, etc.


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Aperiodic sounds

Not all sounds are periodic

Aperiodicsounds are noisy

Their pressure values vary randomly over time

white noise

Interestingly:

White noise sounds the same, no matter how fast or

slow you play it.


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Fricatives

Fricatives are aperiodic speech sounds

[s]

[f]


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Aperiodic Spectra

The power spectrum of white noise has component

frequencies of random amplitude across the board:


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Aperiodic Spectrogram In an aperiodic sound, the values of the component

frequencies also change randomly over time.


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Transients

A transient is: a sudden pressure fluctuation that is not sustained

or repeated over time.

An ideal transient waveform:


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As a matter of fact

Note: white noise and a pure transient are idealizations

We can create them electronically

But they are not found in pure form in nature.

Transient-like natural sounds include:

Hand clapping

Finger snapping Drum beats

Tongue clicking


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Click Waveform

some periodic

reverberationinitial impulse


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Click Spectrum

Reverberation emphasizes some frequencies more than

others


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Click Spectrogram

some periodic

reverberationinitial impulse


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Part 2: Analog and Digital

In reality, sound is analog.

variations in air pressure are

continuous

= it has an amplitude value at allpoints in time.

and there are an infinite number

of possible air pressure values.

Back in the bad old days,

acoustic phonetics was strictly

an analog endeavor.

analog clock


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Part 2: Analog and Digital

In the good new days, we can

represent sound digitallyin a

computer.

!

In a computer, sounds must bediscrete.

everything = 1 or 0 digital clock

Computers represent sounds as

sequences of discrete pressurevalues at separate points in time.

Finite number of pressure values.

Finite number of points in time.


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Analog-to-Digital Conversion

Recording sounds onto a computer requires an analog-to-digital conversion (A-to-D)

When computers record sound, they need to digitize

analog readings in two dimensions:

X: Time (this is called sampling)

Y: Amplitude (this is called quantization)

sampling

quantization


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Sampling Example

0 20 40 60 80 100-100000

1

0

nominal time

amplit

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

Thanks to Chilin Shih for making these materials available.


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Sampling Example


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Sampling Rate Sampling rate = frequency at which samples are taken.

Whats a good sampling rate for speech?

Typical options include:

22050 Hz, 44100 Hz, 48000 Hz

sometimes even 96000 Hz and 192000 Hz

Higher sampling rate preserves sound quality.

Lower sampling rate saves disk space.

(which is no longer much of an issue)

Young, healthy human ears are sensitive to sounds from

20 Hz to 20,000 Hz


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Nyquists Implication

An adequate sampling rate has to be

at least twice as much as any frequency components in

the signal that youd like to capture.

100 Hz sound

200 Hz sampling rate

samples 1 2 3 4 5 6

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Basic Acoustics + DSP