Title: The Mathematics of Signal Processing Series: Cambridge Texts in Applied Mathematics (Book 48) Author: Steven B. Damelin, Willard Miller Jr Format: PDF Hardcover: 462 pages Publisher: Cambridge University Press; 1 edition (January 16, 2012) Language: English ISBN: 978-1107601048

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=Φx 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