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

SPPA 6010 Advanced Speech Science

The Source-Filter Theory: The Sound Source

Topic 3a: Physical Acoustics Review

Learning Objectives

• Outline the physical processes underlying simple harmonic motion using the mass-spring model

• Describe the molecular basis of sound wave propagation

Spring Mass Model

• Mass (inertia)• Elasticity• Friction

What is sound?• It may be defined as the propagation of a

pressure wave in space and time.

• propagates through a medium

Sound-conducting media

• Medium is composed of molecules

• Molecules have “wiggle room”

• Molecules exhibit random motion

• Molecules can exert pressure

Model of air molecule vibration (Time 1)

Rest positions

Air molecules sitting side by side

Model of air molecule vibration

Distance

a b c d

Wave action of molecular motion

Distance

Amplitude waveform

Position

Amplitude waveform

Amplitude

Question: How long will this last?

Model of air molecule vibrationTime

Pressure measuring deviceQuestions: Where is a region of compression?Where is a region of rarefaction?

For example…P

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

Pressure vs. time (pressure waveform)

Pressure

Amplitude

Period (T)

Phase: when a periodbegins

Frequency (F): rate that waveform repeats itself (1/T)

Phase (deg)

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

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

Spatial variation in pressure wave

wavelength () is the distance covering adjacent high and low pressure regions

For example…

Distance

Wavelength ()

Relation between frequency and wavelength

=c/F where

: wavelength

F: is the frequency

c: is sound speed in medium (35,000 cm/sec)

Additional Concepts

• Propagation of waves– Transmission– Absorption– Reflection– Reverberation

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

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

Same sound, different graphs

Time domain

Frequency domain

From Hillenbrand

Classification of sounds

• Number of frequency components– Simple– Complex

• Relationship of frequency components– Periodic– Aperiodic

• Duration– Continuous– Transient

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

Simple periodic sound: Graphic appearance

From Hillenbrand

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

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’

Complex periodic sounds: Graphic appearance

From Hillenbrand

Amplitude vs. Phase Spectrum

Amplitude spectrum: different

Phase spectrum: same

Amplitude vs. Phase Spectrum

Amplitude spectrum: same

Phase spectrum: different

(Complex) Aperiodic sounds

• Complex: > one frequency component

• Aperiodic: Does not repeat itself

• Frequency components are not systematically related

• May be – Continuous– Transient

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’

Aperiodic sounds: Graphic appearance

From Hillenbrand

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

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

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

Waveform envelope

From Hillenbrand

Waveform envelope

Spectrum envelope

From Hillenbrand

Thought Question

Can an aperiodic and complex periodic sound have identical

spectrum envelopes?

Amplitude Spectrum: Window Size

• “short-term” vs. “long-term average” amplitude spectrum

“Instantaneous” Amplitude Spectra

(Long Term) Average Amplitude Spectrum

The Spectrogram

Rotate90 degrees

Rotate it so thatThe amplitude isComing out of thepage

AThis is really narrow because it is a slice in time

Dark bands= amplitudePeaks

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

Highlights harmonic structure

Highlights spectrum envelope

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

What is an “Acoustic” Filter

• holds back (attenuates) certain sounds and lets other sounds through - selective.

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.

Frequency Response Curve (FRC)

Frequencylow high

Center frequency

lower cutofffrequency

upper cutoff frequency

passband

Operation of a filter on a signal

NOTE: Amplitude spectrum describes a soundFrequency response curve describes a filter

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

Low Pass Filters

Frequencylow high

High Pass Filters

Frequencylow high

Band Pass Filter

Frequencylow high

Learning Objectives

• Define resonance, free and forced vibration

• Outline how acoustic resonators behave like acoustic filters

Free vibration

• objects tend to vibrate at a characteristic or resonant frequency (RF)

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

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

Resonance refers to

• Natural vibrating frequency of a system

• The ability of a vibrating system to force another system into vibration

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.

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

Resonator Features

Sharply tuned Broadly tuned

Resonator Features

An example of the resonance characteristics of the human vocal tract

Frequency

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

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