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Mathematical methods and algorithms for signal processing / Todd K. Moon, Wynn C. Stirling

By: Moon, Todd K.
Contributor(s): Stirling, Wynn C [(.j.a)].
Publisher: Upper Saddle River, N.J. : Prentice Hall, c2000Description: xxxvi, 937 p. ; 27 cm.ISBN: 0201361868.Subject(s): Algorithms | Signal processing -- MathematicsDDC classification: 621.38220151
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. - 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. - Bibliography. - Index.
Summary: Mathematical Methods and Algorithms for Signal Processing tackles the challenge many students and practitioners face in the field of signal processing - how to deal with the breadth of mathematical topics employed in the subject. This text provides a solid foundation of theoretical and practical tools that will serve a broad range of signal processing applications. Linear algebra, statistical signal processing, iterative algorithms, and optimization are thoroughly treated, with signal processing examples throughout. Students practicing engineers, and researchers will find Mathematical Methods and Algorithms for Signal Processing useful as a textbook and as a reference. - Back cover
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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. - 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. - Bibliography. - Index.

Mathematical Methods and Algorithms for Signal Processing tackles the challenge many students and practitioners face in the field of signal processing - how to deal with the breadth of mathematical topics employed in the subject. This text provides a solid foundation of theoretical and practical tools that will serve a broad range of signal processing applications. Linear algebra, statistical signal processing, iterative algorithms, and optimization are thoroughly treated, with signal processing examples throughout. Students practicing engineers, and researchers will find Mathematical Methods and Algorithms for Signal Processing useful as a textbook and as a reference. - Back cover

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