Applied and Numerical Harmonic Analysis
1 total work
Time-frequency and time-scale analysis, two of the most important aspects of signal analysis, are developed for the first time in book form as special cases of the more general wave packets. This theory, initiated by Cordoba and Fefferman, has proved to be a valuable tool in operator theory and partial differential equations. Fine decompositions of signals by means of wave packets are also a new and promising tool in signal processing. The book begins with a refresher on basic wavelet and Gabor analysis, followed by the general theory of discrete and continuous wave packets. The presentation is distinguished by its focus on wave packets as objects worthy of independent study.Containing an overview at the beginning of each chapter and many diverse examples, the book may be used as a text for a graduate course or seminar on modern mathematical methods in signal and image processing or applications of harmonic analysis to PDEs. Readers require only a background in real analysis and integration and a certain amount of mathematical maturity, with some familiarity with Gabor and wavelet systems being helpful but not mandatory.
Researchers in pure and applied mathematics, physics, and engineering will also find the work to be an excellent reference.
Researchers in pure and applied mathematics, physics, and engineering will also find the work to be an excellent reference.