Fourier Analysis and Application

In all areas of modelling and numerical simulation, scientists and engineers are faced with problems that require a collection of mathematical tools ranging from the classical-Fourier transforms, convolution, distributions-to the more recent wavelet-based techniques. For this reason, the object of this text, which focuses on Fourier analysis, signal analysis, and filters, is twofold. On the one hand, it conveys to the mathematician a rigorous presentation illustrated with important practical applications of the theory, including a discussion of Fast Fourier Transform. On the other hand it imparts to the physicist and engineer a body of theory in which the well-known formulae find their justification. There is a systematic development of fundamental concepts, such as the Lebesgue integration and theory of distribution, which allows one to establish precise relations among several domains : Fourier transform and convolution ; filtering and sampling; and time-frequency analysis (Gabor transforms and wavelets). Each of the 42 lectures provides an easily assimilated set of ideas and techniques, suitable for both classroom and self-study. Maneuvering through the book is facilitated by grouping the lectures into 12 chapters and by adding numerous summary tables. This latter feature makes the book a handy reference for the subjects covered. Senior undergraduate and graduate students in engineering, physics, and mathematics will find this book helpful. It will also serve as a useful reference for scientists and engineers who deal with modelling and signal processing.