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本帖最后由 cjsb37 于 2013-4-29 09:14 编辑
Mathematical Methods and Algorithms for Signal Processing (Paperback)by Todd K. Moon (Author), Wynn C. Stirling (Author)
Key Phrases: posterior conditional expected loss, cost adjacency matrix, dual approximation problem, Proof Let, Theory of Constrained Optimization, David Hilbert (more...)
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Courses of study There is clearly more information in this book than can be covered in a single semester, or even a full year. Several different courses of study could be devised based on this material, giving instructors the opportunity to choose the material suitable for the needs and development of their students. For example, depending on the focus of the class, instructors might choose to skip completely the numerical aspects of algorithms or, conversely, make them a focus of the course. Several possible course options are described in the following list. In a straightforward overview, the material in the first two parts is regarded as the foundation upon which the major concepts of signal processing are built. The first part provides a review of signal models and representations (e.g., difference equations, transfer functions, state-space form), and introduces several important signal processing problems, such as spectrum estimation and system identification. The second part provides a thorough foundation in linear algebra, working from an undergraduate level up through several applications. Selections from these first two parts, with possible additions from the first appendix on mathematical fundamentals, would make a solid single-semester course in "mathematical methods for signals and systems." A possible course sequence might be as follows: Move fairly quickly through Chapter 1 (with sections 1.8 and 1.10 optional, depending on interest (1-2 weeks)). In Chapter 2, move quickly to the vector-space concepts, then focus on the concept of orthogonality. It may be useful to skip the more technical sections associated with infinite-dimensional vector spaces (for example, sections 2.1.2, 2.1.3, and 2.16). (2 weeks) Spend time in Chapter 3 on least-squares and minimum mean-square filtering and estimation concepts, and the dual approximation problem (sections 3.1-3.14). (2-3 weeks) Depending on interest, examine either wavelet transforms or digital communications from this geometric viewpoint. (1 week) In Chapter 4, focus on sections 4.1-4.5 to get the geometry of the operators, 4.9 for a return to the least-squares idea, and 4.10 for practical computation issues. Introduce the recursive least square filter in section 4.11, and visit partitioned matrix inverses in section 4.12. (2-3 weeks) In Chapter 5, focus on sections 5.2 and 5.3. The QR factorization, in particular, is a foundation for many signal processing algorithms. If a numeric implementation viewpoint is not of interest, then material after section 5.3.5 may be omitted. (2-3 weeks) Sections 6.1-6.5 constitute the principal theory of chapter 6. After these sections have been covered, applications may be drawn from sections 6.76.12, with those in 6.8 and 6.9 probably of the most interest. If a numeric focus is desired, section 6.14 may be covered. (2-3 weeks) The theory of the SVD in sections 7.1-7.5 should be covered, followed by a subset of applications from sections 7.6-7.9. (2-3 weeks) Topics related to special matrices (with special emphasis on Toeplitz matrices) can fill any remaining time. Chapters 10-14 would fit well into a first course on detection and estimation, especially when supplemented by some of the material on linear algebra (such as eigendecompositions and the SVD). This book can be the basis for a one-semester tools course that selects topics from parts I, II, and III. Assuming prior familiarity with continuous-time and discrete-time systems, topics in such a course could include the following. (a) The multivariate Gaussian density (section 1.7). (A course in "iterative methods for signal processing" could focus on chapters in part IV The course material could well be accompanied by a student research project. A course in "methods of optimization for signal processing" could focus on chapters in part V Yet another alternative is a wrap-up course for students in the signals and systems area, who are familiar with their topic areas but wish to sharpen their analytical skills. This course could be similar to the first one outlined, with less time spent in Chapter 1 and more time spent examining numerical implementations. Topics from the last parts of the book could also be selected.
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