2. Speech Science V Akustische Grundlagen WS 2007/8

3. 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

4. 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, 24-44/31-53 Deutsch: c) Pompino-Marschall, Teil II, Ch. 2, 87-101 d) Reetz, Ch. 2, 3-32

5. Air-particle movement Acoustic energy = fluctuating pressure uniform pressure state (all particles equidistant local disturbance moves P1 close to P2 (local pressure increase) P2 moves away from P1, thus moving closer to P3

6. Condensation & rarifaction Pressure changes travel (at the speed of sound!) The pressure change in one area is transmitted to the next …. so the sound moves from its origin and is heard elsewhere This process is called “sound propagation“

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

8. The sinewave The oscillations follow a strict pattern which can be described with a sinusoid function

9. 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 to the 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)

10. Loss of energy (damping) Any “real-world“ vibration will die out because of energy loss (friction)! The more energy loss, the more quickly the signal dies out (the more strongly damped it is) Logarithmically and linearly damped signals

11. 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 the closed phase, but the damping is greater in the open phase

12. Damped glottal cycles Idealized, different degrees of damping would effect the 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.

13. 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

14. 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

15. How complex is the glottal signal? The glottal flow signal is like a rounded sawtooth wave This gives a frequency distribution (spectrum) with all harmonics of the fundamental (F0) present with decreasing power (-12dB per octave)

16. Is the glottal signal like a sawtooth? A square wave has the odd-numbered harmonics The sawtooth wave has every harmonic

17. 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.