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The Mathematics of Signal Processing

Part of Cambridge Texts in Applied Mathematics

  • Date Published: December 2011
  • availability: Available
  • format: Paperback
  • isbn: 9781107601048

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About the Authors
  • 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.

    • Essentially self-contained, so no need to refer to other texts
    • No shortcuts - provides rigorous proofs of fundamental results and also includes over 250 exercises
    • Develops many mathematical tools that can be directly applied to signal processing
    • Students will gain a better appreciation of the relation between pure and applied mathematics
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    Reviews & endorsements

    '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 Reviews

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    Product details

    • Date Published: December 2011
    • format: Paperback
    • isbn: 9781107601048
    • length: 462 pages
    • dimensions: 230 x 152 x 23 mm
    • weight: 0.68kg
    • contains: 50 b/w illus. 265 exercises
    • availability: Available
  • Table of Contents

    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.

  • Instructors have used or reviewed this title for the following courses

    • Applied and Computational Harmonic Analysis
    • Estimation Theory
    • Mathematical Signal Processing
  • Authors

    Steven B. Damelin, Unit for Advances in Mathematics and its Applications, USA
    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, University of Minnesota
    Willard Miller, Jr is Professor Emeritus in the School of Mathematics at the University of Minnesota.

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