Download - 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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What does sound look like?
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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What does sound look like?
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