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Multirate Systems and Filter Banks

Vaidyanathan, P. P. (1993) Multirate Systems and Filter Banks. Prentice Hall Signal Processing Series. Prentice Hall , Upper Saddle River, NJ. https://resolver.caltech.edu/CaltechAUTHORS:20210611-123235747

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[img] PDF (Front Matter) - Published Version
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[img] PDF (Chapter 1. Introduction) - Published Version
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[img] PDF (Chapter 2. Review of Discrete-Time Systems) - Published Version
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[img] PDF (Chapter 3. Review of Digital Filters) - Published Version
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[img] PDF (Chapter 4. Fundamentals of Multirate Systems) - Published Version
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[img] PDF (Chapter 5. Maximally Decimated Filter Banks) - Published Version
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[img] PDF (Chapter 6. Paraunitary Perfect Reconstruction (PR) Filter Banks) - Published Version
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[img] PDF (Chapter 7. Linear Phase Perfect Reconstruction QMF Banks) - Published Version
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[img] PDF (Chapter 8. Cosine Modulated Filter Banks) - Published Version
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[img] PDF (Chapter 9. Quantization effects) - Published Version
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[img] PDF (Chapter 10. Multirate filter bank theory and related topics) - Published Version
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[img] PDF (Chapter 11. The wavelet transform and its relation to multirate filter banks) - Published Version
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[img] PDF (Chapter 12. Multidimensional Multirate Systems) - Published Version
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[img] PDF (Chapter 13. Review of Discrete-Time Multi-Input Multi-Output LTI Systems) - Published Version
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Abstract

Multirate digital signal processing techniques have been practiced by engineers for more than a decade and a half. This discipline finds applications in speech and image compression, the digital audio industry, statistical and adaptive signal processing, numerical solution of differential equations, and in many other fields. It also fits naturally with certain special classes of time-frequency representations such as the short-time Fourier transform and the wavelet transform, which are useful in analyzing the time-varying nature of signal spectra. Over the last decade, there has been a tremendous growth of activity in the area of multirate signal processing, perhaps triggered by the first book in this field [Crochiere and Rabiner, 1983]. Particularly impressive is the amount of new literature in digital filter banks, multidimensional multirate systems, and wavelet representations. The theoretical work in multirate filter banks appears to have reached a level of maturity which justifies a thorough, unified, and in-depth treatment of these topics. This book is intended to serve that purpose, and it presents the above mentioned topics under one cover. Research in the areas of multidimensional systems and wavelet transforms is still proceeding at a rapid rate. We have dedicated one chapter to each of these, in order to bring the reader up to a point where research can be begun. I have always believed that it is important to appreciate the generality of principles and to obtain a solid theoretical foundation, and my presentation here reflects this philosophy. Several applications are discussed throughout the book, but the general principles are presented without bias towards specific application-oriented detail. The writing style here is very much in the form of a text. Whenever possible I have included examples to demonstrate new principles. Many design examples and complete design rules for filter banks have been included. Each chapter includes a fairly extensive set of homework problems (totaling over 300). The solutions to these are available to instructors, from the publisher. Tables and summaries are inserted at many places to enable the reader to locate important results conveniently. I have also tried to simplify the reader’s task by assigning separate chapters for more advanced material. For example, Chap. 11 is dedicated to wavelet transforms, and Chap. 14 contains detailed developments of many results on paraunitary systems. Whenever a result from an advanced chapter (for example, Chap. 14) is used in an earlier chapter, this result is first stated clearly within the context of use, and the reader is referred to the appropriate chapter for proof. The text is self-contained for readers who have some prior exposure to digital signal processing. A one-term course which deals with sampling, discrete-time Fourier transforms, z-transforms, and digital filtering, is sufficient. In Chap. 2 and 3 a brief review of this material is provided. A thorough exposition can be found in a number of references, for example, [Oppenheim and Schafer, 1989]. Chapter 3 also contains some new material, for example, eigenfilters, and detailed discussions on allpass filters, which are very useful in multirate system design. A detailed description of the text can be found in Chap. 1. Chapters 2 and 3 provide a brief review of signals, systems, and digital filtering. Chapter 4, which is the first one on multirate systems, covers the fundamentals of multirate building blocks and filter banks, and describes many applications. Chapter 5 introduces multirate filter banks, laying the theoretical foundation for alias cancelation, and elimination of other errors. The first two sections in Chap. 4 and 5 contain material overlapping with [Crochiere and Rabiner, 1983]. Most of the remaining material in these chapters, and in the majority of the chapters that follow, have not appeared in this form in text books. Chapters 6 to 8 provide a deeper study of multirate filter banks, and present several design techniques, including those based on the so-called paraunitary matrices. (These matrices play a role in the design of many multirate systems, and are treated in full depth in Chap. 14.) Chapters 9 to 12 cover special topics in multirate signal processing. These include roundoff noise effects (Chap. 9), block filtering, periodically time varying systems and sampling theorems (Chap. 10), wavelet trans-forms (Chap. 11) and multidimensional multirate systems (Chap. 12). Chapters 13 and 14 give an in-depth coverage of multivariable linear systems and lossless (or paraunitary) systems, which are required for a deeper understanding of multirate filter banks and wavelet transforms. There are five appendices which serve as references as well as supplementary reading. Three of these are review-material (matrix theory, random processes, and Mason’s gain formula). Two of the appendices contain results directly related to filter bank systems. One of these is a technique for spectral factorization; the other one analyzes the effects of quantization of subband signals. Many of these chapters have been taught at Caltech over the last three years. This text can be used for teaching a one, two, or three term (quarter or semester) course on one of many possible topics, for example, multirate fundamentals, multirate filter banks, wavelet representation, and so on. There are many homework problems. The instructor has a great deal of flexibility in ch∞sing the topics, but I prefer not to bias him or her by providing specific course outlines here. In summary, I have endeavored to produce a text which is useful for the class-room, as well as for self-study. It is also hoped that it will bring the reader to a point where he/she can start pursuing research in a vast range of multirate areas. Finally, I believe that the text can be comfortably used by the practicing engineer because of the inclusion of several design procedures, examples, tables, and summaries.


Item Type:Book
ORCID:
AuthorORCID
Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Prentice Hall. Rights reverted to P. P. Vaidyanathan. The generous support and pleasant environment offered by the California Institute of Technology has been most crucial in the successful completion of this project. The funding provided by the National Science Foundation for our research in multirate signal processing has been very helpful in developing many of the results which are included in this text. I also take this opportunity to thank Prof. Alan Oppenheim for his enthusiasm about this project, and for including this text in his distinguished signal processing series. I am indebted to Brendan Stewart, Prentice Hall, for carefully supervising the production of the final book. Karen Gettman, Prentice Hall, was very helpful during all stages of the writing process. Several professional colleagues and students have played a major role in the evolution and completion of this project. Professor Maurice Bellanger (TRT, France), and Drs. Ron Crochiere, N. S. Jayant, and Larry Rabiner of the AT&T Bell Lab-oratories, provided the valuable encouragement which I needed during the initial stages. I am deeply thankful to Dr. Rabiner for his criticism of the first draft, and for providing many valuable suggestions on the style of presentation. His feedback has resulted in significant improvement of the presentation here. My heartfelt gratitude also goes to Prof. Martin Vetterli (Columbia University, New York) for his great enthusiasm, interaction, friendship, and valuable feedback over the years, and to Professors Mark Smith and Tom Barnwell (Georgia Institute of Technology), for their constant support. Prof. Smith had studied the first draft of the manuscript very carefully, and provided valuable suggestions. I am indebted to Dr. Ajay Luthra and his colleagues (Tektronix laboratories), for their enthusiasm and interest in the project. Some of the research work related to this book has been done with the support from Tektronix. Dr. Rashid Ansari (Bellcore), Prof. Roberto Bamberger (Washington State University) and Dr. Jelena Kovačević (AT& T Bell laboratories) provided valuable comments on the chapter on multidimensional multirate systems. Dr. Ingrid Daubechies (AT& T Bell laboratories) provided very useful feedback, which improved parts of Chap. 11 (wavelets) substantially. Ramesh Gopinath (Rice University) also provided important comments on this chapter. I also wish to thank Prof. Tom Parks (Cornell University) for his valuable feedback on Chap. 1 to 6 and 11, Prof. P. K. Rajan (Tennesse Technological University) for his comments on Chap. 12, and Prof. A. Sideris (Caltech) for comments on Chap. 13. I appreciate the interest shown by Prof. H. Malvar (University of Brasilia), Prof. George Moschytz (Swiss Federal Institute of Technology), and Prof. Tor Ramstad (Norwegian Institute of Technology). I also sincerely acknowledge the constant moral support and encouragement I received from Prof. Sanjit Mitra (University of California, Santa Barbara) during various stages. Several graduate students at Caltech have participated in the research that eventually gave rise to this book. In this regard, my interactions with Tsuhan Chen, Zinnur Doğanata, Phuong-Quan Hoang, David Koilpillai, Vincent Liu, Truong Nguyen, Vinay Sathe, and Anand Soman have been most enjoyable. David’s research at Caltech has had a major effect on Chap. 8 (cosine modulated filter banks). In addition to providing intellectual interactions at the deepest level, Tsuhan Chen, David Koilpillai, Truong Nguyen, and Anand Soman have also generated many of the multirate design examples in this text. They have also read various chapters of the manuscript and provided useful feedback. In this connection my special thanks go to Tsuhan Chen, Zinnur Doğanata, Ian Galton, David Koilpillai, Ramesh Rajaram, Ken Rose and Anand Soman for reading many of the chapters. Tsuhan was a very careful reader, and provided many valuable suggestions for Chap. 12. Ian Galton provided several comments on writing style as well as technical contents, which I found to be extremely useful. Ian’s enthusiasm and friendship are gratefully acknowledged. Debbie McGougan and Cynthia Stewart at Caltech were very helpful during various phases of the manuscript preparation. Solutions to all the homework problems have been prepared by Tsuhan Chen, Igor Djokovic, See-May Phoong, and Anand Soman. I appreciate their interest and patience. My parents have been responsible for teaching me many valuable “theorems of life” which I could not find in text books and papers. These certainly were the principles which sustained me during all phases of this project. My deepest gratitude goes to my wife Usha who showed infinite patience and understanding during my absorption in this long project, and offered the type of moral support and loving encouragement which only she can offer. Countless were the evenings, weekends, and holidays during which she provided me with the seclu-sion and peace of mind needed to pursue this ambitious goal. She is certainly my best blessing, and this book would have remained an idle dream without her support. P. P. Vaidyanathan California Institute of Technology
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