SPPA 6010 Advanced Speech Science 1 The Source-Filter Theory: The Sound Source.

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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9



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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

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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

SPPA 6010 Advanced Speech Science 1 The Source-Filter Theory: The Sound Source.

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Transcript of SPPA 6010 Advanced Speech Science 1 The Source-Filter Theory: The Sound Source.