Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets (Texts in Applied Mathematics) Book

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 - the Fourier transform, 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 two-fold. 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, that allows one to establish precise relations among several domains: Fourier transform and convolution; filtering and sampling; 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 or 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.Read More