Mathematical Methods and Algorithms for Signal Processing

Description:

For Senior/Graduate Level Signal Processing courses. The book is also suitable for a course in advanced signal processing, or for self-study.

Mathematical Methods and Algorithms for Signal Processing tackles the challenge of providing students 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.

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.