The mathematics of signal processing / Steven B. Damelin, Willard Miller, Jr.

Format:

Book

Author/Creator:

Damelin, Steven B., author.

Miller, Willard, author.

Series:

Cambridge texts in applied mathematics ; 48.

Cambridge texts in applied mathematics ; 48

Language:

English

Subjects (All):

Signal processing--Mathematics.

Signal processing.

Physical Description:

1 online resource (xii, 449 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2012.

Language Note:

English

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.

Contents:

Preface

Introduction

1. Normed vector spaces

2. Analytic tools

3. Fourier series

4. The Fourier transform

5. Compressive sampling

6. Discrete transforms

7. Linear filters

8. Windowed fourier and continuous wavelet transforms. Frames

9. Multiresolution analysis

10. Discrete wavelet theory

11. Biorthogonal filters and wavelets

12. Parsimonious representation of data.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. [437]-442) and index.

ISBN:

1-107-22943-X

1-280-77480-0

1-139-22281-3

9786613685193

1-139-22452-2

1-139-21801-8

1-139-00389-5

1-139-21492-6

OCLC:

806042075