Morlet wavelets and the phase vocoder applied to musical sound transformation

One of the primary challenges of musical signal processing entails discovering methods of producing sounds which are new, unique, and perhaps unattainable through conventional acoustic orchestration, but which have attributes of conven-tional instruments, imparting a sense of non-mechanical "realness" to the listener. The Phase Vocoder, an analysis / resynthesis approach, allows us to analyze the time/frequency components of a sampled sound and reconstruct the sound as a sum of time-varying frequencies, like additive synthesis. Since we may start by sampling rich sounds, the sense of "realness" may be encoded into the analysis. The Phase Vocoder approach then allows us to analyze the phase and amplitude components of the particular frequencies we're interested in and modify these in various ways, such as "cross-synthesis" techniques combining the frequency com-ponents of one sound with the amplitude components of another, time-stretching and compression of sound without frequency modification, or frequency shifting without time-stretching/ compression. We investigate the use of the Phase Vocoder in this context, using the Morlet wavelet transform rather than the short-time Fourier transform in the analysis phase, with the overall goal of implementing such a system on a personal com-puter. Morlet wavelets are more efficient in terms of amount of frequency bands needed, and hence time required for analysis, over the same overall bandwidth, and seem to better respect the auditory system's response to sound, due to octave scaling, allowing for better time resolution for high frequencies and better fre-quency resolution for low frequencies. We then explore the various modifications allowed by the Phase Vocoder in resynthesizing sounds.