Wavelet methods for estimation of acoustically relevant parameters of musical signals
Richard Kronland-Martinet, Ph. GUILLEMAIN, A. Grossmann · The Journal of the Acoustical Society of America · 1990
Wavelet transforms are a class of analysis and resynthesis methods that have been found useful in a variety of domains [Wavelets, edited by J. M. Combes, A. Grossmann, and Ph. Tehamitchian (Springer-Verlag, IPTI, 1989)]. They provide a two-dimensional (time and scale) description of one-dimensional signals. In this paper, wavelet transforms are used as the basis for an algorithm that represents an audio signal as a sum of “spectral components” (contributions obtained by amplitude modulation and slow frequency modulation around a frequency). A central role in this construction is played by the phase of the (complex-valued) wavelet transform; the interpretation of this phase is particularly simple and intuitive if the analyzing wavelet is chosen as an analytic signal (progressive wavelet). The parameters determined by the algorithm allow an additive reconstruction of the signal, as well as a variety of nonlinear modifications. These possibilities will be illustrated by several audio examples.