SPPA 6010 Advanced Speech Science
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The Source-Filter Theory: The Sound Source
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Topic 3a: Physical Acoustics Review
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Learning Objectives
• Outline the physical processes underlying simple harmonic motion using the mass-spring model
• Describe the molecular basis of sound wave propagation
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Spring Mass Model
• Mass (inertia)• Elasticity• Friction
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What is sound?• It may be defined as the propagation of a
pressure wave in space and time.
• propagates through a medium
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Sound-conducting media
• Medium is composed of molecules
• Molecules have “wiggle room”
• Molecules exhibit random motion
• Molecules can exert pressure
A B
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Model of air molecule vibration (Time 1)
Rest positions
Air molecules sitting side by side
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Model of air molecule vibration (Time 2)
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Model of air molecule vibration (Time 3)
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Model of air molecule vibration (Time 4)
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Model of air molecule vibration (Time 5)
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Model of air molecule vibration
Time
1
2
3
4
5
Distance
a b c d
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Wave action of molecular motion
Time
1
2
3
4
5
Distance
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Amplitude waveform
Position
Time
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Amplitude waveform
Amplitude
Time
Question: How long will this last?
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Model of air molecule vibrationTime
1
2
3
4
5
Pressure measuring deviceQuestions: Where is a region of compression?Where is a region of rarefaction?
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For example…P
ress
ure
Time
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Learning Objectives
• Define the key characteristics of sinusoidal motion (amplitude, frequency/period and phase)
• Outline the relationship between the frequency and wavelength of a sound wave
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Pressure vs. time (pressure waveform)
Pressure
Time
Amplitude
Period (T)
Phase: when a periodbegins
Frequency (F): rate that waveform repeats itself (1/T)
Phase (deg)
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Phase
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Initiating a sound waves that differ only in phase
A force is applied to molecule at frequency f and time t
same force applied at frequency f at time t+a where a < the period of vibration
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Features of a pressure waveform
• Amplitude– Measured in pressure units– peak amplitude– peak-to-peak amplitude– Instantaneous amplitude
• Period and Frequency– Period measured in time (basic quantity)– Frequency is a rate measure (per unit time) expressed as Hertz
(s-1)– May be expressed as octaves, semitones, etc
• Phase– Measured in degrees (relative to period length)– 0-360 degrees
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Spatial variation in pressure wave
wavelength () is the distance covering adjacent high and low pressure regions
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For example…
Distance
Wavelength ()
Pre
ssur
e
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Relation between frequency and wavelength
=c/F where
: wavelength
F: is the frequency
c: is sound speed in medium (35,000 cm/sec)
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Additional Concepts
• Propagation of waves– Transmission– Absorption– Reflection– Reverberation
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Learning Objectives
• Draw and describe time-domain and frequency-domain representation of sound
• Distinguish between simple and complex sound sounds with regard to physical characteristics and graphical representations
• Distinguish between periodic and aperiodic sounds with specific emphasis on terms such as fundamental frequency/period, harmonics, and overtones
• Distinguish between continuous and transient sounds • Describe how waves sum, define Fourier's theorem and
be able to describe the basics of Fourier analysis
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Graphic representation of sound
• Time domain– Called a waveform– Amplitude plotted as
a function of time
• Frequency domain– Called a spectrum– Amplitude spectrum
• amplitude vs. frequency
– Phase spectrum• phase vs. frequency
– May be measured using a variety of “window” sizes
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Same sound, different graphs
Time domain
Frequency domain
From Hillenbrand
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Classification of sounds
• Number of frequency components– Simple– Complex
• Relationship of frequency components– Periodic– Aperiodic
• Duration– Continuous– Transient
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Simple periodic sound
• Simple: one frequency component• Periodic: repeating pattern• Completely characterized by
– amplitude– period (frequency)– phase
• Other names: sinusoid, simple harmonic motion, pure tone
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Simple periodic sound: Graphic appearance
From Hillenbrand
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Complex periodic sounds
• Complex: > one frequency component• Periodic: repeating pattern• Continuous• Frequencies components have a special relation
– Lowest frequency: fundamental frequency
• Symbol: fo
• Frequency component with longest period
– Higher frequency components: harmonics • integer (whole number) multiples of the fo
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Complex periodic sounds: Graphic appearance
• Time domain:– repeating pattern of pressure change– within the cycle, things look complex
• Frequency domain: – spectral peaks at evenly spaced frequency
intervals – “picket fence” appearance
• Auditory impression: sounds ‘musical’
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Complex periodic sounds: Graphic appearance
From Hillenbrand
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Amplitude vs. Phase Spectrum
Amplitude spectrum: different
Phase spectrum: same
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Amplitude vs. Phase Spectrum
Amplitude spectrum: same
Phase spectrum: different
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(Complex) Aperiodic sounds
• Complex: > one frequency component
• Aperiodic: Does not repeat itself
• Frequency components are not systematically related
• May be – Continuous– Transient
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Aperiodic sounds: Graphic appearance
• Time domain:– no repeating pattern of pressure change
• Frequency domain:– the spectrum is dense – No “picket fence”
• Auditory impression: sounds ‘noisy’
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Aperiodic sounds: Graphic appearance
From Hillenbrand
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Analysis of complex waves
• Waves can be summed• Complex waves are the sum of simple waves• Fourier: French Mathematician:
– Any complex waveform may be formed by summing sinusoids of various frequency, amplitude and phase
• Fourier Analysis– Provides a unique (only one) solution for a given sound signal– Is reflected in the amplitude and phase spectrum of the signal– Reveals the building blocks of complex waves, which are
sinusoids
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Learning Objectives
• Draw and differentiate the waveform and the waveform envelope
• Draw and differentiate the amplitude spectrum, the phase spectrum and the spectrum envelope
• Differentiate between short-term and long-term average amplitude spectra
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The “envelope” of a sound wave
• Waveform envelope:– imaginary smooth line that follows the peak of
the amplitude of a sound pressure waveform
• Spectrum envelope:– Imaginary smooth line drawn on top of the
amplitude spectrum
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Waveform envelope
From Hillenbrand
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Waveform envelope
Time
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Spectrum envelope
From Hillenbrand
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Thought Question
Can an aperiodic and complex periodic sound have identical
spectrum envelopes?
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Amplitude Spectrum: Window Size
• “short-term” vs. “long-term average” amplitude spectrum
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“Instantaneous” Amplitude Spectra
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(Long Term) Average Amplitude Spectrum
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The Spectrogram
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Rotate90 degrees
F
A F
A
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Rotate it so thatThe amplitude isComing out of thepage
F
AThis is really narrow because it is a slice in time
F
Time
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Dark bands= amplitudePeaks
Time
Fre
quen
cy
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Two main types of spectrograms
• Wide-band spectrograms– Akin to spectrum envelopes “lined up”– Frequency resolution not so sharp
• Narrow-band spectrograms– Akin to amplitude spectrums “lined up”– Frequency resolution is really sharp
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Highlights harmonic structure
Highlights spectrum envelope
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Learning Objectives
• Define an acoustic filter• Draw and label a frequency response curve• Draw and differentiate different types of acoustic
filters• Define terms such as cutoff frequency, center
frequency, roll off rate, gain, and bandwidth• Define and draw a basic filter system and relate
that to the source-filter theory of speech production
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What is an “Acoustic” Filter
• holds back (attenuates) certain sounds and lets other sounds through - selective.
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Why might we be interested in filters?
• Human vocal tract acts like a frequency selective acoustic filter
• Human auditory system behaves as a frequency selective filter
• helps us understand how speech is produced and perceived.
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Frequency Response Curve (FRC)
Frequencylow high
Gai
n
+
-
Center frequency
lower cutofffrequency
upper cutoff frequency
passband
3 dB
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Operation of a filter on a signal
NOTE: Amplitude spectrum describes a soundFrequency response curve describes a filter
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Kinds of frequency selective filters
Low-pass filters– Lets low frequencies “pass through” and attenuates
high frequencies
High-pass filters– Lets high frequencies “pass through” and attenuates
low frequencies
Band-pass filters– Lets a particular frequency range “pass through” and
attenuates other frequencies
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Low Pass Filters
Frequencylow high
Gai
n
+
-
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High Pass Filters
Frequencylow high
Gai
n
+
-
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Band Pass Filter
Frequencylow high
Gai
n
+
-
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Learning Objectives
• Define resonance, free and forced vibration
• Outline how acoustic resonators behave like acoustic filters
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Free vibration
• objects tend to vibrate at a characteristic or resonant frequency (RF)
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Forced vibration
• A vibrating system can force a nearby system into vibration
• The efficiency with which this is accomplished is related to the similarity in the resonant frequency (RF) of the two systems
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Forced vibration
• If the RF of the two systems are the same, the amplitude of forced vibration will be large
• If the RF of the two systems are quite different, the amplitude of forced vibration will be small or nonexistent
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Resonance refers to
• Natural vibrating frequency of a system
• The ability of a vibrating system to force another system into vibration
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Resonance
Acoustic (Cavity) Resonators
• Transmit sound frequencies with more or less efficiency, depending upon the physical characteristics
• Therefore, they act as filters, passing through (and even amplifying) some frequencies and attentuating others.
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Resonance
Acoustic (Cavity) Resonators• And since they act as filters, they have most
of the same features of a filter, even though we might use different names.
• Center frequency is often termed the resonant frequency.
• Frequency response curve often termed the resonance curve.
• Resonators may be sharply or broadly “tuned” which refers to the roll-off frequency
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Resonator Features
Sharply tuned Broadly tuned
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Resonator Features
An example of the resonance characteristics of the human vocal tract
Frequency
Gain