Multirate Statistical Signal Processing

ISBN-13: 9781402053160 / Angielski / Twarda / 2007 / 172 str.

Omid S. Jahromi

Opis

The ?eld of multirate signal processing has witnessed a great deal of progress and an increasingly wide range of applications since the publication of the ?rst textbook by Crochiere and Rabiner (1983). However, this progress has been mainly in the area of deterministic systems with emphasis on perfe- reconstruction and/or orthogonal systems. This book introduces a statistical theory for extracting information from signals that have di?erent sampling rates. This new theory generalizes the conventional (deterministic) theory of multirate systems beyond many of its constraints.Furthermore, itallowsfortheformulationofseveralnewproblems such as spectrum estimation, time-delay estimation and sensor fusion in the realm of multirate signal processing. I have arrived at the theory presented here by integrating concepts from diverse areas such as information theory, inverse problems and theory of - equalities. The process of merging a variety of concepts of di?erent origin results in both merits and shortcomings. The former include the fresh and - di?erentiated view of an amateur, providing scope of application. The latter include a lack of in-depth experience in each of the original ?elds. Granted, this may lead to gaps in continuity, however it goes without saying that a complete theory can seldom be achieved by one person and in a short time. My goal in writing this book has been to inspire the reader to initiate his own research and add to the theory of multirate statistical signal processing

Recenzje

From the reviews:

"The book presents the set of results, obtained by a thorough study of a variety of signal processing problems ... . The main goal of the author in writing this book is to inspire the reader to initiate his own research ... . The book will be of interest for all specialists working in the area of digital signal processing. It will be very useful for the students, postgraduates and researchers, which are looking for new directions of their studies."(Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1141, 2008)

Spis treści

1. Introduction. 1.1. Multi-channel multirate signal measurement. 1.2. Multirate statistical signal processing. 1.3. Notation. 2. Background. 2.1. Second-order theory of stationary stochastic processes. 2.2. Statistical inference and information. 2.3. Theory of majorization. 2.4. Inverse problems, ill-posedness and Tikhonov’s theory of regularization. 3. Multirate Spectrum Estimation. 3.1. Introduction. 3.2. Formulating the inference problem. 3.3. The Maximum Entropy principle. 3.4. Solving Problem 2. 3.5. On well-posedness of the Maximum Entropy solution. 3.6. Practical considerations. 3.7. Examples. 3.8. Discussion on the Maximum Entropy formalism. 3.9. Concluding remarks. 4. Multirate Time Delay Estimation. 4.1. Introduction. 4.2. Time-Delay Estimation in Multirate Sensor Arrays. 4.3. Fusion of Low-rate Signals In The Presence Of Time Delay. 4.4. Designing The Synthesis Filters. 4.5. Procedure for designing multirate sensor arrays. 4.6. Concluding Remarks. 4.7. Proof of Theorem 1. 4.8. Proof of Theorem 2. 4.9. Perfect reconstruction linear-phase filter banks. 5. Multirate Signal Estimation. 5.1. Introduction. 5.2. Problem Statement. 5.3. Statistics of the non-observable vector X and the measurement vector V. 5.4. Estimating X given V. 5.5. Discussion. 5.6. Putting everything together. 5.7. Concluding remarks. 6. Algebraic Theory of Scalable Multirate Systems. 6.1. Introduction. 6.2. FIR analysis and synthesis systems. 6.3. Scalability in multirate systems. 6.4. Embedding partial ordering of scalability in a total ordering. 6.5. SC-Optimality and Subband Coding. 6.6. SC-Optimality and the Principal Component Filter Bank. 6.7. Concluding remarks. 6.8. Summary. 7. Information Theory of Multirate Systems. 7.1. Introduction. 7.2. The information content of a low-rate measurement. 7.3. Measuring statistical information in practice. 7.4.Scalability in terms of information. 7.5. Concluding remarks and open problems. 8. Distributed Algorithms. 8.1. Introduction. 8.2. Spectrum estimation using sensor networks. 8.3. Inverse and Ill-posed problems. 8.4. Spectrum estimation using generalized projections. 8.5. Distributed algorithms for calculating generalized projection. 8.6. Concluding remark. 8.7. Acknowledgements. 9. Epilogue.

O autorze

Omid S. Jahromi, Ph.D., is the Principal Engineer at Authorizer Technologies in Palm Beach Gardens, Florida. He has extensive academic and industrial research experience in the fields of digital signal processing, image processing and biometric identity verification.

Dr. Jahromi has taught several engineering courses at the departments of Electrical and Computer Engineering and Mechanical and Industrial Engineering at the University of Toronto in Toronto, Canada. Since 2004, he has been leading several standardization projects at the American National Standards Institute (ANSI) and the International Organization for Standards (ISO) focusing on the standardization of biometric data interchange formats.