The Mathematics of Signal Processing

by Damelin, Steven, B.; Miller, Willard, Jr.

• ISBN13: 9781107601048
• ISBN10: 1107601045
• Format: Paperback
• Copyright: 2012-01-31
• Publisher: Cambridge Univ Pr

Summary

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.

Table of Contents

Introduction

Normed vector spaces

Analytic tools

Fourier series

Fourier transforms

Compressive sensing

Discrete transforms

Linear filters

Windowed Fourier transforms, continuous wavelets, frames

Multiresolution analysis

Discrete wavelet theory

Biorthogonal filters and wavelets

Parsimonious representation of data

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.