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Mathematical Methods and Algorithms for Signal Processing, 1st edition

  • Todd K. Moon
  • Wynn C. Stirling

Published by Pearson (August 4th 1999) - Copyright © 2000

1st edition

Mathematical Methods and Algorithms for Signal Processing

ISBN-13: 9780201361865

Includes: Paperback
Free delivery
$165.32 $206.65

What's included

  • Paperback

    You'll get a bound printed text.

Overview

Mathematical Methods and Algorithms for Signal Processing tackles the challenge of providing readers and practitioners with the broad tools of mathematics employed in modern signal processing. Building from an assumed background in signals and stochastic processes, the book provides a solid foundation in analysis, linear algebra, optimization, and statistical signal processing.

FEATURES/BENEFITS

  • Many MATLAB algorithms and examples.
    • Allow the reader to understand more deeply by seeing the implementation and to learn by doing.
  • A strong foundation which motivates the development of advanced concepts, removing the "mysteries" frequently encountered by users—Geometric insight is presented wherever possible.
    • Readers develop maturity to read literature, and develop confidence in their abilities. Ex. Ch. 2, 3
  • Solid introduction to wavelets in the context of vector spaces—Including transform algorithms and basic theory.
    • Presents this important and modern topic in a context that should help the readers understanding. Ex. Ch. 3
  • Interesting modern topics not available in many other signal processing texts—Such as the EM algorithm, blind source separation, projection on convex sets, etc., in addition to many more conventional topics such as spectrum estimation, adaptive filtering, etc.
    • Motivate reader interest by presenting the field as dynamic, with an enormous number of useful applications.
  • Review of many signal models, in time domain, frequency domain, and state space domain, showing relationships between them, and issues related to their applications.
    • Readers can learn to move among the various forms, and understand how they relate. Also, come to understand the importance of a good signal model in approaching new problems. Ex. Ch. 1
  • Presents path algorithms (dynamic programming and Viterbi) with many applications.
  • Coverage of detection and estimation theory.
    • Learning to employ the tools they have gained in the first part, overcoming some of the algebraic difficulties frequently encountered in this area. Ex. Ch. 10
  • More than one approach to some problems.
    • In QR factorization and the Kalman filter, for example, multiple approaches are presented so the reader can gain insight and approach the realization that there is more than one way to solve the most interesting problems. Ex. Ch. 5, 14

Table of contents

I. INTRODUCTION AND FOUNDATIONS.

 1. Introduction and Foundations.

II. VECTOR SPACES AND LINEAR ALGEBRA.

 2. Signal Spaces.

 3. Representation and Approximation in Vector Spaces.

 4. Linear Operators and Matrix Inverses.

 5. Some Important Matrix Factorizations.

 6. Eigenvalues and Eigenvectors.

 7. The Singular Value Decomposition.

 8. Some Special Matrices and Their Applications.

 9. Kronecker Products and the Vec Operator.

III. DETECTION, ESTIMATION, AND OPTIMAL FILTERING.

10. Introduction to Detection and Estimation, and Mathematical Notation.

11. Detection Theory.

12. Estimation Theory.

13. The Kalman Filter.

IV. ITERATIVE AND RECURSIVE METHODS IN SIGNAL PROCESSING.

14. Basic Concepts and Methods of Iterative Algorithms.

15. Iteration by Composition of Mappings.

16. Other Iterative Algorithms.

17. The EM Algorithm in Signal Processing.

V. METHODS OF OPTIMIZATION.

18. Theory of Constrained Optimization.

19. Shortest-Path Algorithms and Dynamic Programming.

20. Linear Programming.

APPENDIXES.

A. Basic Concepts and Definitions.

B. Completing the Square.

C. Basic Matrix Concepts.

D. Random Processes.

E. Derivatives and Gradients.

F. Conditional Expectations of Multinomial and Poisson r.v.s.

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