W v e l e t s and Sianal U

avelet theory provides a unified framework for a number of techniques which had been developed inde-pendently for various signal processing applications. For ex-ample, multiresolution signal processing, used in computer vision; subband coding, developed for speech and image compression; and wavelet series expansions, developed in applied mathematics, have been recently recognized as different views of a single theory. In fact, wavelet theory covers quite a large area. I t treats both the continuous and the discrete-time cases. I t provides very general techniques that can be applied to many tasks in signal processing, and therefore has numerous potential applications. In particular, the Wavelet Transform (WT) is of inter-est for the analysis of non-stationary signals, because it provides an alternative to the classical Short-Time Fourier Transform (STFT) or Gabor transform [GAE346, ALL77, POR801. The basic difference is as follows. In contrast to the STET, which uses a single analysis window, the WT uses short windows at high frequencies and long windows at low frequencies. This is in the spirit of so-called “constant-Q ” or constant relative bandwidth frequency analysis. The WT is also related to time-frequency analysis based on the Wigner-Ville distribution [FLA89, FLASO, RIOSOal. For some applications it is desirable to see the WT as a signal decomposition onto a set of basis functions. In fact, basis functions called wauelets always underlie the wavelet analysis. They are obtained from a single prototype wavelet by dilations and contractions (scal