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Basic Acoustics + Digital Signal Processing. January 14, 2014. 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.

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just so you know
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?
part 1 an acoustic dichotomy
Part 1: An Acoustic Dichotomy
  • Acoustically speaking, there are two basic kinds of sounds:
  • 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
the third wheel
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
  • Let’s look at the acoustic properties of each type of sound in turn…
acoustics basics
Acoustics: Basics
  • How is a periodic sound transmitted through the air?
  • Consider a bilabial trill:

Fad

Pin

Fad

what does sound look like
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?
what does sound look like1
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 back past its initial rest position

initial rest position

what does sound look like2
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
compression wave
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!
compression wave1
Compression Wave

area of high pressure

(compression)

area of low pressure

(rarefaction)

  • Compression waves consist of alternating areas of high and low pressure
pressure level meters
Pressure Level Meters
  • Microphones
    • Have diaphragms, which move back and forth with air pressure variations
    • Pressure variations are converted into electrical voltage
  • 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
measuring sound
Measuring Sound
  • What if we set up a pressure level meter at one point in the wave?

Time

pressure level meter

sine waves
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.

pressure

time

other basic sinewave concepts
Other Basic Sinewave concepts
  • Sinewaves are periodic; i.e., they recur over time.
  • The period is the amount of time it takes for the pattern to repeat itself.
  • A cycle is one repetition of the acoustic pattern.
  • The frequency is 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 peakamplitude is the the maximum amount of vertical displacement in the wave
    • = maximum (or minimum) amount of pressure
waveforms
Waveforms
  • A waveform plots air pressure on the y axis against time on the x axis.
phase shift
Phase Shift
  • Even if two sinewaves have the same period and amplitude, they may differ in phase.
  • Phase essentially describes where in the sinewave cycle the wave begins.
  • This doesn’t affect the way that we hear the waveform.
  • Check out: sine waves vs. cosine waves!
complex waves
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 of these values.
    • Ac(t1) = A1 (t1) + A2 (t1)
complex wave example
Complex Wave Example
  • Take waveform 1:
    • high amplitude
    • low frequency

+

  • Add waveform 2:
    • low amplitude
    • high frequency

=

  • The sum is this complex waveform:
a real life example
A Real-Life Example
  • 480 Hz tone
  • 620 Hz tone
  • the combo = ?
spectra
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
one way to look at it
One Way to Look At It
  • Combining 100 Hz and 1000 Hz sinewaves results in the following complex waveform:

amplitude

time

the other way
The Other Way
  • The same combination of 100 Hz and 1000 Hz sinewaves results in the following power spectrum:

amplitude

frequency

the third way
The Third Way
  • A spectrogram shows how the spectrum of a complex sound changes over time.

time

frequency

1000 Hz

100 Hz

  • intensity (related to amplitude) is represented by shading in the z-dimension.
fundamental frequency
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.
aperiodic sounds
Aperiodic sounds
  • Not all sounds are periodic
  • Aperiodic sounds 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.
fricatives
Fricatives
  • Fricatives are aperiodic speech sounds

[s]

[f]

aperiodic spectra
Aperiodic Spectra
  • The power spectrum of white noise has component frequencies of random amplitude across the board:
aperiodic spectrogram
Aperiodic Spectrogram
  • In an aperiodic sound, the values of the component frequencies also change randomly over time.
transients
Transients
  • A transient is:
    • “a sudden pressure fluctuation that is not sustained or repeated over time.”
  • An ideal transient waveform:
a transient spectrum
A Transient Spectrum
  • An ideal transient spectrum is perfectly flat:
as a matter of fact
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
click waveform
Click Waveform

some periodic reverberation

initial impulse

click spectrum
Click Spectrum
  • Reverberation emphasizes some frequencies more than others
click spectrogram
Click Spectrogram

some periodic reverberation

initial impulse

part 2 analog and digital
Part 2: Analog and Digital
  • In “reality”, sound is analog.
    • variations in air pressure are continuous
    • = it has an amplitude value at all points in time.
    • and there are an infinite number of possible air pressure values.

analog clock

  • Back in the bad old days, acoustic phonetics was strictly an analog endeavor.
part 2 analog and digital1
Part 2: Analog and Digital
  • In the good new days, we can represent sound digitally in a computer.
  •  In a computer, sounds must be discrete.
    • everything = 1 or 0

digital clock

  • Computers represent sounds as sequences of discrete pressure values at separate points in time.
  • Finite number of pressure values.
  • Finite number of points in time.
analog to digital conversion
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)

quantization

sampling

sampling rate
Sampling Rate
  • Sampling rate = frequency at which samples are taken.
  • What’s 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
one consideration
One Consideration
  • The Nyquist Frequency
    • = highest frequency component that can be captured with a given sampling rate
    • = one-half the sampling rate

Harry Nyquist (1889-1976)

  • Problematic Example:
  • 100 Hz sound
  • 100 Hz sampling rate

samples 1 2 3

nyquist s implication
Nyquist’s Implication
  • An adequate sampling rate has to be…
    • at least twice as much as any frequency components in the signal that you’d like to capture.
  • 100 Hz sound
  • 200 Hz sampling rate

samples 1 2 3 4 5 6