Victor Wickerhauser has suggested that wavelet packets could be useful in sound synthesis (13). His idea is that a single wavelet packet generator could replace a large number of oscillators. Through experimentation, a musician could determine combinations of wave packets that produce especially interesting sounds.
Wickerhauser feels that sound synthesis is a natural use of wavelets. Say one wishes to approximate the sound of a musical instrument. A sample of the notes produced by the instrument could be decomposed into its wavelet packet coefficients. Reproducing the note would then require reloading those coefficients into a wavelet packet generator and playing back the result. Transient characteristics such as attack and decay- roughly, the intensity variations of how the sound starts and ends- could be controlled separately (for example, with envelope generators), or by using longer wave packets and encoding those properties as well into each note. Any of these processes could be controlled in real time, for example, by a keyboard.
Notice that the musical instrument could just as well be a human voice, and the notes words or phonemes.
A wavelet-packet-based music synthesizer could store many complex sounds efficiently because
- wavelet packet coefficients, like wavelet coefficients, are mostly very small for digital samples of smooth signals; and
- discarding coefficients below a predetermined cutoff introduces only small errors when we are compressing the data for smooth signals.
Similarly, a wave packet-based speech synthesizer could be used to reconstruct highly compressed speech signals. Figure 8 illustrates a wavelet musical tone or toneburst.
Fig. 8. Wavelets for music: a graphical representation of a Wickerhauser toneburst. This screenshot of a toneburst was taken while it was playing in the Macintosh commercial sound program Kaboom! Factory. (Toneburst courtesy Victor Wickerhauser)
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