Time-Frequency/Time-Scale Analysis

Originally published in French as Temps-frequence, this book is a multi-disciplinary introduction to the toos of time-frequency signal analysis (often referred to as wavelet analysis). It serves as an invaluable reference for anyone concerned with the application of these techniques to signal processing.Although Fourier analysis provides a natural environment for the description of stationary signals, most real signals are nonstationary. Indeed, most often an integral part of the information contained in a signal can be found in the nonstationary property itself (e.g., start and termination of events, drifts, ruptures, modulations). This book provides a coherent and self-contained presentation of a broad panorama of methods for analyzing nonstationary signals, an area which has recently undergone intensive development in signal processing. Special emphasis is given to non-parametric approaches, with particular focus on quadratic energy distributions. This book offers a discussion of problems that emerge from a mixed description in time and frequency, and it comprises a detailed construction of the principle classes of admissible solutions (short-time Fourier, wavelets, Wigner-Ville, Cohen's class, affine distributions, etc.). It also addresses numerous issues of interpretation related to such representations and shows how to reformulate several important problems in signa theory by utilizing joint time-frequency distributions.