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An introduction to signal detection and estimation
Signal Processing20 (1990) 95-100 Elsevier
95
BOOK REVIEWS
" Multiplicative Complexity, Convolution, and the
DFT", by M.T. HEIDEMAN, Publishers: Springer-Verlag GmbH & Co. KG, Heidelberger Platz 3, Berlin, 1988, viii + 155 pp., ISBN 3-540-96810-5
This book is a survey of the theory of multiplicative complexity in digital signal processing and largely based on the results of S. Winograd during the last two decades. The need for a rigorous theory of multiplicative complexity is well justified. A theoretical analysis of the multiplicative complexity of a system may not lead to the best practical algorithms but, in any case, deepens one's understanding of the system and gives bounds for possible improvements of existing suboptimal algorithms. The basic theory of multiplicative complexity is developed in Chapter 2 and applied to bilinear and quadratic systems. In Chapter 3 the author covers general results of multiplicative complexity of systems of polynomial multiplication which includes convolution and DFT. In the last parts of Chapter 3 the results are extended for polynomials of several variables. From Chapter 4 on, the book concentrates on more and more specific systems, polynomial products with constraints, one-dimensional D F T and D F T with input con-
"An Introduction to Signal Detection and Estimation", by H. Vincent POOR, Department of Elec-
trical and Computer Engineering, University of Urbana-Champaign, U.S.A., Publishers: SpringerVerlag, New York, Inc., U.S.A., 1988, x + 549 pp., ISBN 0-387-96667-6
straints. In the end of the book there are four appendixes; the basic properties of cyclotomic polynomials, programs for computing multiplicative complexities and tables of multiplicative complexities of specific systems. A set of problems is also included. The book is an extension of the author's thesis and it contains a large amount of material on multiplicative complexity in a systematically developed form. It is a good reference for anyone working in the field. Some background in algebra and number theory is necessary to be able to read the book as concepts like homomorphisms, field extensions and residue class rings are used but not defined. Bearing this in mind the book can also be used as an introduction to the theory of multiplicative complexity. Even though the author has added examples and comments, the book's origin as a thesis aimed at specialists limits its pedagogical value. Also, as the notations are (unavoidably) complex an inclusion of a glossary of terms and notations would have improved readability. Jaakko ASTOLA Tampere University P.O. Box 607 33101 Tampere Finland
The book is adapted from a course taught at the University of Illinois. The author warns the reader in the preface that he should have a working knowledge of applied probability and random processes. Such a prerequisite is very necessary to follow the
96
Book reviews
extensive and complete mathematical developments presented in this book. The purpose of the book is to introduce the reader to the fundamentals of detection and estimation theory and the classical theoretical results are developed in a very complete and consistent way. The book is structured as follows: I. Notation II. Elements of hypothesis testing III. Signal detection in discrete time IV. Elements of parameter estimation V. Elements of signal estimation VI. Signal detection in continuous time VII. Signal estimation in continuous time After a short presentation of the notation used in the book the author develops systematically the theoretical foundation of signal detection and estimation in noise. Chapter II presents and compares the Bayesian, the Minimax and the Neyman-Pearson Hypothesis Testing. This chapter gives a short but complete overview of these three classical basic results applied to binary hypothesis-testing with some indications to their generalisation for M-ary cases. These results are then consistently applied in the rest of the book. Another simplification is given by considering only discrete time signals. The continuous cases are treated in Chapters VI and VII. Chapter III discusses various models of optimum detector structures based on the three methods of Chapter II. Some useful design methods for sequential, robust and nonparametric detection are also presented. Although Chapter III is the longest of the book, more developments relative to information theory and signal characteristics would be welcome. Basically the book is mostly based on Radar Signal Detection. The extension of these results to bit conditioners used in digital communications would also be interesting. Parameter Estimation is the subject of Chapter IV where two basic approaches are presented: the Bayesian in which the parameter is assumed to be Signal Processing
a random quantity related statistically to the observation, and a second in which the parameter is assumed to be unknown but without being endowed with any probability structures. Some more practical Signal Estimation examples would help the reader of the practice to better follow the theoretical results developed in this chapter. Time-varying signals are introduced in Chapter V and a very good development of signal estimation and tracking is presented. In particular the presentations of Kalman-Bucy and WienerKolmogorov Filtering are very clear and comprehensive. Again, examples in the data communications area would be appreciated, in particular when presenting the linear prediction filter. Continuous time signals are treated in Chapters VI and VII, and the notion of function space is introduced to model such problems. The reader is assumed to be familiar with the mathematics necessary to cover theoretical developments such as the theory of integration in abstract spaces. The Karhunen-Lo~ve expansion is used to show the equivalence to discrete-time processes. In the Signal Estimation cases treated in Chapter VII linear/Gaussian estimation is performed for the linear assumption. The treatment of more complex cases such as nonlinear filtering are also outlined. A very interesting presentation of the Continuous-Time Kalman-Bucy Filter is given at the end of the book. In summary the book is very well suited for a complete and systematic introduction to the basic theory of signal detection and estimation. It assumes a solid knowledge of the reader in the area of basic mathematics and probability theory. The engineer of the practice may miss the applications of the theory presented in this book to very practical cases, specially in the area of data communications over non-linear channels or in presence of non gaussian noise. J.G. G A N D E R Eichstrasse 6 4708 Luterbach Switzerland
95
BOOK REVIEWS
" Multiplicative Complexity, Convolution, and the
DFT", by M.T. HEIDEMAN, Publishers: Springer-Verlag GmbH & Co. KG, Heidelberger Platz 3, Berlin, 1988, viii + 155 pp., ISBN 3-540-96810-5
This book is a survey of the theory of multiplicative complexity in digital signal processing and largely based on the results of S. Winograd during the last two decades. The need for a rigorous theory of multiplicative complexity is well justified. A theoretical analysis of the multiplicative complexity of a system may not lead to the best practical algorithms but, in any case, deepens one's understanding of the system and gives bounds for possible improvements of existing suboptimal algorithms. The basic theory of multiplicative complexity is developed in Chapter 2 and applied to bilinear and quadratic systems. In Chapter 3 the author covers general results of multiplicative complexity of systems of polynomial multiplication which includes convolution and DFT. In the last parts of Chapter 3 the results are extended for polynomials of several variables. From Chapter 4 on, the book concentrates on more and more specific systems, polynomial products with constraints, one-dimensional D F T and D F T with input con-
"An Introduction to Signal Detection and Estimation", by H. Vincent POOR, Department of Elec-
trical and Computer Engineering, University of Urbana-Champaign, U.S.A., Publishers: SpringerVerlag, New York, Inc., U.S.A., 1988, x + 549 pp., ISBN 0-387-96667-6
straints. In the end of the book there are four appendixes; the basic properties of cyclotomic polynomials, programs for computing multiplicative complexities and tables of multiplicative complexities of specific systems. A set of problems is also included. The book is an extension of the author's thesis and it contains a large amount of material on multiplicative complexity in a systematically developed form. It is a good reference for anyone working in the field. Some background in algebra and number theory is necessary to be able to read the book as concepts like homomorphisms, field extensions and residue class rings are used but not defined. Bearing this in mind the book can also be used as an introduction to the theory of multiplicative complexity. Even though the author has added examples and comments, the book's origin as a thesis aimed at specialists limits its pedagogical value. Also, as the notations are (unavoidably) complex an inclusion of a glossary of terms and notations would have improved readability. Jaakko ASTOLA Tampere University P.O. Box 607 33101 Tampere Finland
The book is adapted from a course taught at the University of Illinois. The author warns the reader in the preface that he should have a working knowledge of applied probability and random processes. Such a prerequisite is very necessary to follow the
96
Book reviews
extensive and complete mathematical developments presented in this book. The purpose of the book is to introduce the reader to the fundamentals of detection and estimation theory and the classical theoretical results are developed in a very complete and consistent way. The book is structured as follows: I. Notation II. Elements of hypothesis testing III. Signal detection in discrete time IV. Elements of parameter estimation V. Elements of signal estimation VI. Signal detection in continuous time VII. Signal estimation in continuous time After a short presentation of the notation used in the book the author develops systematically the theoretical foundation of signal detection and estimation in noise. Chapter II presents and compares the Bayesian, the Minimax and the Neyman-Pearson Hypothesis Testing. This chapter gives a short but complete overview of these three classical basic results applied to binary hypothesis-testing with some indications to their generalisation for M-ary cases. These results are then consistently applied in the rest of the book. Another simplification is given by considering only discrete time signals. The continuous cases are treated in Chapters VI and VII. Chapter III discusses various models of optimum detector structures based on the three methods of Chapter II. Some useful design methods for sequential, robust and nonparametric detection are also presented. Although Chapter III is the longest of the book, more developments relative to information theory and signal characteristics would be welcome. Basically the book is mostly based on Radar Signal Detection. The extension of these results to bit conditioners used in digital communications would also be interesting. Parameter Estimation is the subject of Chapter IV where two basic approaches are presented: the Bayesian in which the parameter is assumed to be Signal Processing
a random quantity related statistically to the observation, and a second in which the parameter is assumed to be unknown but without being endowed with any probability structures. Some more practical Signal Estimation examples would help the reader of the practice to better follow the theoretical results developed in this chapter. Time-varying signals are introduced in Chapter V and a very good development of signal estimation and tracking is presented. In particular the presentations of Kalman-Bucy and WienerKolmogorov Filtering are very clear and comprehensive. Again, examples in the data communications area would be appreciated, in particular when presenting the linear prediction filter. Continuous time signals are treated in Chapters VI and VII, and the notion of function space is introduced to model such problems. The reader is assumed to be familiar with the mathematics necessary to cover theoretical developments such as the theory of integration in abstract spaces. The Karhunen-Lo~ve expansion is used to show the equivalence to discrete-time processes. In the Signal Estimation cases treated in Chapter VII linear/Gaussian estimation is performed for the linear assumption. The treatment of more complex cases such as nonlinear filtering are also outlined. A very interesting presentation of the Continuous-Time Kalman-Bucy Filter is given at the end of the book. In summary the book is very well suited for a complete and systematic introduction to the basic theory of signal detection and estimation. It assumes a solid knowledge of the reader in the area of basic mathematics and probability theory. The engineer of the practice may miss the applications of the theory presented in this book to very practical cases, specially in the area of data communications over non-linear channels or in presence of non gaussian noise. J.G. G A N D E R Eichstrasse 6 4708 Luterbach Switzerland