Understanding Speech: Source-Filter Theory & Larynx Vibrations, Study notes of Linguistics

Download Understanding Speech: Source-Filter Theory & Larynx Vibrations and more Study notes Linguistics in PDF only on Docsity!

Source-Filter Theory

Speech: dual vibration system

Larynx (source)

• Folds vibrate in an infinite number of modes like strings
• produces oscillations of air pressure.
• Modes are the harmonics of the voiced source.

Supralaryngeal tube (filter)

• Air molecules in tube are set into vibration by air pressure fluctuations caused by larynx.
• Air in the tube functions as another mass-spring system. Molecules vibrate in an infinite number of modes, which are the formants.
• What determines mode frequencies?

Sound Source

sentence from siSwat'i (Southern Bantu language; Swaziland)

electroglottograph (EGG) signal recorded from

subject's larynx while sentence is being produced.

(This is what it would sound like if the larynx did

not have a neck and head attached to it).

Modulation in period of glottal wave carries

intonation (pitch).

Why is does the source spectrum look like that?

.01 .02.

Components of (physical) dynamical systems: springs Physical understanding: components of dynamical systems: springs I (^) Displace a spring from its resting position (stretch or compress) and it returns smoothly. I (^) Sti↵ness of spring determines how quickly it returns: slinky vs. your skin. I (^) Rule for change: Change in x = kx I (^) k is related to the sti↵ness of the spring. 0 5 10 15 − 100 − 80 − 60 − 40 − 20 0 20 40 60 80 100 Time Money in Bank -. -. -. -. Linguistics 580 (USC Linguistics) Modes in Source and Filter October 20, 2015 2 / 23

Spring vs. Mass+Spring

7 Spring vs. mass+spring Spring: Change in x = 1 2 x 0 5 10 15 0 10 20 30 40 50 60 70 80 90 100 Time Water in bathtub 0 5 10 15 20 25 30 − 1 −0. −0. −0. −0. 0

1 Time Position Mass+Spring

Changing Mass and Stiffness

What is the effect of changing spring stiffness on

frequency? Why?

What is the effect of changing mass on frequency?

Why?

Demonstration:

https://www.walter-fendt.de/html5/phen/springpendulum_en.htm

Modes

Principle 2 I (^) For every mass that is added, an additional mode is found. I (^) A string can be divided into an infinite number of masses, so can oscillate at an infinite number of frequencies Crucial Ideas:

• There are as many modes as there are masses.
• In the lower modes, the system is behaving as if it has fewer masses than it actually has.
• A string can be divided into an infinite number of masses, so can oscillate at an infinite number of frequencies

Larynx as Vibrating string

A string attached at two ends

can be thought of as composed

of an an infinite number of

masses connected by springs.

Infinite number of modes.

Each higher mode has a

frequency that is an integer

multiple of the lowest mode.

Larynx is like a vibrating string

(or pair of strings).

Modes of string vibrations

• In this example, string is set into motion by driving it at the mode frequencies, one at time.
• If we were to pluck the string, it would actually vibrate at all of the modes at the same time.
• Note that the higher the mode, the lower the amplitude (why?)
• Passing air through the larynx is like plucking a string. It vibrates at all modes at once.
• Note amplitudes of laryngeal modes (=harmonics)!

Speech: dual vibration system

Larynx (source)

Supralaryngeal tube (filter)

• Air molecules in tube are set into vibration by air pressure fluctuations caused by larynx.
• Air in the tube functions as another mass-spring system. Molecules vibrate in an infinite number of modes, which are the formants.
• Constrictions (produced by gestures of lips, tongue tip, tongue body, and velic systems) act to change the mode frequencies.
• Thus, the gestures leave their "signatures" in the sound that escapes the mouth.
• Purely mechanical models can produce sounds like those produced by a human vocal tract.

Wave Propagation

• Wave motion: Disturbance of particles in an elastic medium from equilibrium position (x 0 ) can propagate through to particles that are coupled to the site of the disturbance, and then to particles that are coupled to those... etc..
• Transverse Waves: Particle motion is at right angles to direction of wave propagation.
• Longitudinal Waves: Particle motion is along the axis of wave propagation. Animations courtesy of Dr. Dan Russell, Kettering University Particles oscillate over only short distances, but pattern of motion propagates over long distance https://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

Superposition of waves Animation courtesy of Dr. Dan Russell, Kettering University https://www.acs.psu.edu/drussell/Demos/superposition/ superposition.html

Waves traveling in opposite

directions superpose when they

coincide, then continue traveling.

Oscillations of the same

frequency, and same amplitude

form standing waves when they

superpose.

• Don’t travel, only change in

amplitude over time.

• Nodes:^ no change in position.
• Anti-nodes:^ maximal change in

position.

NODE ANTI- NODE

Modes of vibration of air in tubes

Air vibrating in a tube is like many masses connected by springs.

For visualization, first consider a tube that is closed at both ends. There will be modes of vibration like those of a string attached at both ends

In the lowest mode, all the molecules move together (in the same direction), like our one-mass demo, and like lowest mode of the string.

Like string, the masses near the middle moves most, the masses at the ends move less. ibrating in a tube is like many masses connected by springs. visualization, first consider a tube that is closed at both ends. re will be modes of vibration like those of a string. e lowest mode, all the molecules move together (in the same ction), like our two- and three-mass demos, and like lowest m e string. string, the masses near the middle moves most, the masses a ends move less.

Lowest two modes of air vibration

olecules vibrating in a tube: lowest two modes of d tube cs 285 (USC Linguistics) Lecture 11: Understanding /IY/ and /AA/ Formants October 15, 2017 10 / 14 Like lowest 2 modes of two-mass system