Speech Science V

Akustische Grundlagen

WS 2007/8

Recapitulation

• Airstream production (pulmonic, glottal or velaric airstreams serve as a basis for speech sound production)

• The kinetic airstream energy can be transformed into acoustic energy at various points along the vocal tract.

• The first point at which the transformation can occur is at the glottis (the space between the vocal folds)

• The acoustic energy is periodic if the vocal folds vibrate, aperiodic if they are constricted but do not vibrate

Topics

• What are sounds physically? • Periodic signals - sinusoids• Damping - phonation• Complex waveforms

Reading: a) Kent, Ch. 2, 22-34 b) Borden, Harris & Raphael, Ch. 3, 24-44/31-

53Deutsch: c) Pompino-Marschall, Teil II, Ch. 2, 87-101

d) Reetz, Ch. 2, 3-32

Air-particle movement

• Acoustic energy = fluctuating pressure

uniform pressure state (all particles equidistant

local disturbance moves P1 closeto P2 (local pressure increase)

P2 moves away from P1, thus moving closer to P3

Condensation & rarifaction

• Pressure changes travel (at the speed of sound!)

The pressure change in one areais transmitted to the next ….

so the sound moves from itsorigin and is heard elsewhere

This process is called “sound propagation“

Periodic signals

• A disturbed air particle oscillates through its resting point and back (just like any other vibrating system):

The sinewave

• The oscillations follow a strict pattern which can be described with a sinusoid function

D = A sin Ωt where

Ω = 2 π/T

Calculating the amplitude

• The momentary amplitude D is determined by the position on the circumference (which is equivalent tothe angle of the radius line to that point):

D = sin or:

D = A sin 2 π t/T or: = position on the circumference of the circle. (which changes with time)

Loss of energy (damping)

• Any “real-world“ vibration will die out because of energy loss (friction)!

The more energyloss, the more quickly the signaldies out (the morestrongly damped it is)

Logarithmically and linearly damped signals

What has this to do with speech?

• The acoustic energy from the vocal-fold vibrations is strongly damped

• Each glottal closure adds energy to the system, which quickly weakens.

Negative pressure is created by the abrupt closure of the vocal folds. The oscillation is visible during theclosed phase, but thedamping is greater inthe open phase

Damped glottal cycles

• Idealized, different degrees of damping would effectthe speech signal as the following figure shows

In both signals the glottal impulse renews the energy after 5 oscillations, but in the left signal damping is weak and the oscillations have continued strongly; in the right signal damping is strong and the oscillations have

almost died out.

Complex signals

• What aspect of the glottal signal oscillates (and is therefore damped)?

• The glottal signal is NOT a single sinusoid (i.e. not energy at one single frequency)

• When the vocal folds vibrate and come together (each glottal cycle), they produce an impulse with harmonic energy

• These “harmonics“ are vibrations at every multiple of the fundamental glottal frequency

F0 = 100 Hz; Harmonics = 100, 200, 300, 400, 500, 600 ……. Hz

At any point in time, the overall amplitude (energy) is the sum of the component amplitudes

What do complex

signals look like?

E-synth demo

How complex is the glottal signal?

The glottal flowsignal is like arounded sawtoothwave

This gives a frequency distribution (spectrum)with all harmonics of the fundamental (F0)present with decreasingpower (-12dB per octave)

Is the glottal signal like a sawtooth?

A square wave has the odd-numberedharmonics

The sawtooth wavehas every harmonic

Summary

• Local fluctuations of air pressure (air-particle proximity) = acoustic energy

• These are propagated at the speed of sound

• Repeated patterns of pressure change are „periodic signals“

• The simplest waveform is the sinusoidal wave, which can be described with a simple mathematical function

• Complex waves can be described as a sum of simple waves

• The glottal wave is the sum of all the harmonics of the fundamental frequency

• The glottal wave is very heavily damped; each glottal closure brings fresh energy into the system.