The Wavelet Transform for Analysis, Synthesis, and Processing of Speech and Music Sounds

Abstract

The wavelet transform is a recent method of signal analysis and synthesis (Grossmann and Morlet 1984; Grossmann et al. 1987). It analyzes signals in terms of wavelets-functions limited both in the time and the frequency domain. In comparison, the classical Fourier analysis method analyzes signals in terms of sine and cosine wave components that are not limited in time. The wavelet transform is related to granular analysis/synthesis, first suggested by Gabor (1946). Granular synthesis has been implemented by Roads (1978) and Truax (1988). Rodet (1985) and Li6nard (1984) use adapted grains for speech signals; however, these implementations do not attempt to reconstruct an arbitrary given signal. The Gabor method uses an expansion of a function into a two-parameter family of elementary wavelets that are obtained from one basic wavelet