1 Acoustics DSP

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Basic Acoustics +

Digital Signal Processing

September 11, 2014



Road Map! • 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

•

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



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…



Pin

Fad

Fad

• How is a periodic sound transmitted through the air?

• Consider a bilabial trill:

Acoustics: Basics



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?




• 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




• 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

•

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 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

• 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



Measuring Sound

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

wave?

Time

pressure level meter



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



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 peak amplitude is the the maximum amount of

vertical displacement in the wave

•

= maximum (or minimum) amount of pressure



Waveforms

•

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



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 doesn’t affect the way that we hear the waveform.

• Check out: sine waves vs. cosine 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 ofthese values.

• Ac(t1) = A1 (t1) + A2 (t1)



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

• 480 Hz tone

• 620 Hz tone

• the combo = ?



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 •

Combining 100 Hz and 1000 Hz sinewaves results in

the following complex waveform:

a

m

pl

i

tu

de

time



The Other Way

•

The same combination of 100 Hz and 1000 Hz

sinewaves results in the following power spectrum:

a

m

pl

i

tu

de

frequency



The Third Way

•

A spectrogram shows 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



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. (boring!)

• GCD of 480 and 620 Hz is 20.

• GCD of 600 and 800 Hz is 200, etc.



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 are aperiodic speech sounds

[s]

[f]



Aperiodic Spectra

•

The power spectrum of white noise has component

frequencies of random amplitude across the board:



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

frequencies also change randomly over time.



Transients

•

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

or repeated over time.”

• An ideal transient waveform:



A Transient Spectrum

• An ideal transient spectrum is perfectly flat:



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

some periodic

reverberation

initial impulse



Click Spectrum

• Reverberation emphasizes some frequencies more than

others



Click Spectrogram

some periodic

reverberation

initial impulse



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



Part 2: Analog and Digital

• In the good new days, we can

represent sound digitally in 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.



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



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.



Sampling Example



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

•

The Nyquist Frequency

• = highest frequency component that

can be captured with a given sampling

rate

• = one-half the sampling rate

Problematic Example:• 100 Hz sound

• 100 Hz sampling rate

samples 1 2 3

Harry Nyquist

(1889-1976)



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



Sampling Rate Demo

• Speech should be sampled at at least 44100 Hz

• (although there is little frequency information in speech

above 10,000 Hz)

• 44100 Hz

• 22050 Hz

•

11025 Hz (watch out for [s])

• 8000 Hz

•

5000 Hz

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1 Acoustics DSP