Introduction to Speech Acoustics 2

1. Harmonics and Spectra

(a) Complex waves can be mathematically analysed as being composed of different sine waves (Fourier analysis). Vibrating objects don't usually vibrate at a single frequency, they have harmonics.

(b) According to when each harmonic starts, the different elements of a complex wave can be in different phase relations (N.B. the human ear is not thought to be sensitive to phase relations).

(c) Very important: any complex wave can be analysed into the periodic elements of different frequencies of which it is composed. Result: the spectrum of sound. For example, the following spectrum is of the waveform produced at the glottis in a vowel. Note the series of peaks or harmonics, occurring at integer multiples of the fundamental frequency f0.

Fig. 1

(Click on the graph to hear an imitation of the sound that comes out of the larynx.)

(d) Non-periodic sounds are more adequately represented not by line spectra but by a continuous spectrum.

Fig. 2: Continuous spectra of non-periodic sounds: left [s] (peak at c. 5920 Hz); right [ʃ] (peak at c. 2700 Hz). 2. Resonators and Filters

(a) Natural frequencies and resonance - different objects more or less tuned to specific frequencies - can act as filters.

Filters have centre frequency and bandwidth - the range of frequencies passed by filter not more than 3dB down on its maximum amplitude. The bandwidth of a filter may be relatively narrow or broad.

3. Source + Filter theory: Vowel Sounds

(a) The vocal tract acts as a complex variable filter. Into this is input a signal from the glottal source (for voiced sounds). Fig 1 shows a glottal source wave for a vowel, i.e. a complex wave with numerous harmonics which rapidly decrease in amplitude as frequency increases (12 dB/octave).

(b) Vowel sounds seen as product of glottal source and variable filtering effect of supraglottal tract. So, the same vowels have the same gross spectral shape, irrespective of the fundamental frequency f0 of the source.

Fig. 1 filtered once ...

filtered twice ...

and filtered 3 times

Fig. 3: Spectrum of a vowel sound shown as the product of the glottal source and the filtering effect of the supraglottal vocal tract. (Click on the graphs to hear the results of filtering.)