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 of sounds: 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…

P in F ad 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?

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 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 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 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 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 on the x axis.

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 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. A 1 (t 1 ) := Amplitude value of sinewave 1 at time 1 A 2 (t 1 ) := Amplitude value of sinewave 2 at time 1 The amplitude value of the complex wave is the sum of these values. A c (t 1 ) = A 1 (t 1 ) + A 2 (t 1 )

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: amplitudeamplitude time

The Other Way The same combination of 100 Hz and 1000 Hz sinewaves results in the following power spectrum: amplitudeamplitude frequency

The Third Way A spectrogram shows how the spectrum of a complex sound changes over time. frequencyfrequency time intensity (related to amplitude) is represented by shading in the z-dimension 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 all points 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 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 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 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: Hz, Hz, Hz sometimes even Hz and 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 Harry Nyquist ( )

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

Sampling Rate Demo Speech should be sampled at at least Hz (although there is little frequency information in speech above 10,000 Hz) Hz Hz Hz (watch out for [s]) 8000 Hz 5000 Hz