The Mathematics of Signal Processing

Develops mathematical and probabilistic tools needed to give rigorous derivations and applications of fundamental results in signal processing theory.

Steven B. Damelin (Author), Willard Miller, Jr (Author)

9781107601048, Cambridge University Press

Paperback / softback, published 15 December 2011

462 pages, 50 b/w illus. 265 exercises
23 x 15.2 x 2.3 cm, 0.68 kg

'In the last 20 years or so, many books on wavelets have been published; most of them deal with wavelets from either the engineering or the mathematics perspective, but few try to connect the two viewpoints. The book under review falls under the last category … Overall, the book is a good addition to the literature on engineering mathematics.' Ahmed I. Zayed, Mathematical Reviews

Arising from courses taught by the authors, this largely self-contained treatment is ideal for mathematicians who are interested in applications or for students from applied fields who want to understand the mathematics behind their subject. Early chapters cover Fourier analysis, functional analysis, probability and linear algebra, all of which have been chosen to prepare the reader for the applications to come. The book includes rigorous proofs of core results in compressive sensing and wavelet convergence. Fundamental is the treatment of the linear system y=?x in both finite and infinite dimensions. There are three possibilities: the system is determined, overdetermined or underdetermined, each with different aspects. The authors assume only basic familiarity with advanced calculus, linear algebra and matrix theory and modest familiarity with signal processing, so the book is accessible to students from the advanced undergraduate level. Many exercises are also included.

1. Introduction
2. Normed vector spaces
3. Analytic tools
4. Fourier series
5. Fourier transforms
6. Compressive sensing
7. Discrete transforms
8. Linear filters
9. Windowed Fourier transforms, continuous wavelets, frames
10. Multiresolution analysis
11. Discrete wavelet theory
12. Biorthogonal filters and wavelets
13. Parsimonious representation of data
Bibliography
Index.

Subject Areas: Signal processing [UYS], Numerical analysis [PBKS]