Mathematical Methods and Algorithms for Signal Processing

TODD K. MOON is currently with the Electrical and Computer Engineering department at Utah State University, where he has taught widely in the area of signals and systems, including signal processing, communications, controls, and information theory. His research interests have included signal separation, spread-spectrum communication, wavelet modulation, speech processing, and signal reconstruction. WYNN C. STIRLING is a professor of electrical engineering at Brigham Young University, where he has served on the faculty since 1984. He received his Ph.D. in electrical engineering from Stanford University, and has worked as a research engineer for Rockwell International Corporation, ESL, Inc. (now TRW), and Autonetics. His research interests include decision theory, control theory, estimation theory, and stochastic processes. Dr. Stirling has contributed numerous articles to professional journals, and is a member of IEEE and Phi Beta Kappa.

• 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.