~velets and Signal Processing

velet theory provides a unified framework for a number of techniques which had been developed independently for various signal processing applications. For example. 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. It treats both the continuous and the discrete-time cases. It 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 (Wf) is of interest for the analysis of non-stationary signals, because it provides an altemative to the classical Short-Time Fourier Transform (STFT) or Gabor transform [GAB46, ALL77, POR80]. The basic difference is as follows. In contrast to the STFT, 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-QH or constant relative bandwidth frequency analysis. The WT is also related to time-frequency analysis based on the Wigner-Ville distribution [FLA89, FLA90, RI090a].