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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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## Basic Acoustics + Digital Signal Processing

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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. • Any questions so far?**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**• 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**• How is a periodic sound transmitted through the air? • Consider a bilabial trill: Fad Pin Fad**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. pressure time**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**• 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. • 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**• 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: amplitude time**The Other Way**• The same combination of 100 Hz and 1000 Hz sinewaves results in the following power spectrum: amplitude frequency**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**• 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**• 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. analog clock • Back in the bad old days, acoustic phonetics was strictly an analog endeavor.**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) quantization sampling**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 Harry Nyquist (1889-1976) • Problematic Example: • 100 Hz sound • 100 Hz sampling rate samples 1 2 3**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

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