The Mathematics of Signal Processing
1st Edition
Published on 24. October 2014
978-1-139-21148-2 (ISBN)
Description
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.
Reviews / Votes
'Damelin and Miller provide a very detailed and thorough treatment of all the important mathematics related to signal processing. This includes the required background information found in elementary mathematics courses, so their book is really self-contained. The style of writing is suitable not only for mathematicians, but also for practitioners from other areas. Indeed, Damelin and Miller managed to write their text in a form that is accessible to nonspecialists, without giving up mathematical rigor.' Kai Diethelm, Computing Reviews '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 ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 30 Halftones, unspecified; 20 Line drawings, unspecified
File size
3,24 MB
ISBN-13
978-1-139-21148-2 (9781139211482)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Steven B. Damelin | Willard Miller, Jr
The Mathematics of Signal Processing
Book
12/2011
Cambridge University Press
€168.50
Shipment within 15-20 days
Persons
Steven B. Damelin is currently Full Professor at Georgia Southern University and Visiting Full Professor at the University of the Witwatersrand in Johannesburg. Willard Miller, Jr is Professor Emeritus in the School of Mathematics at the University of Minnesota.
Content
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.
