[3] J. I. Aunon and C. D. McGillem, "Techniques for processing single evoked ... Only a few years ago, books on digital signal processing were appearing.
IEEE TRANSACTIONS ON SYSTEMS,
white noise. A suboptimum inverse filter using the known distortion transfer function and only an approximate knowledge of the signal bandwidth is then used as the final step in the estimation procedure. It is shown that this filter gives better results than the previously formulated Wiener estimator. Furthermore, this filter does not require a large number of responses for the estimation of signal and noise characteristics as required previously reported estimators. Points that need further investigation are the general applicability of the estimator, possible suboptimum time-domain solutions to the inverse filtering stage, and the sensitivity of the filter output to the assumed signal spectrum. REFERENCES [1] N. W. Perry and D. G. Childers, The Human Visual Evoked Response. Springfield, IL: Charles C. Thomas, 1969. [2] J. B. Krauss, "Computerized average response and autocorrelation methods as related to signal detection in noise," in Data Acquisition and Processing in Biology and Medicine, vol. 3, K. Enslein, Ed. New York: Pergamon, 1964.
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[3] J. I. Aunon and C. D. McGillem, "Techniques for processing single evoked
potentials," Trans. San Diego Biomed. Symp., pp. 211-218, 1975. [4] T. Nogawa, et al., "Visual evoked potentials estimated by Wiener filtering," Electroenceph. Clin. Neurophysiol., vol. 35, pp. 375-378, 1973. [5] D. 0. Walter, "A posteriori Wiener filtering of average evoked responses," Electroenceph. Clin. Neurophysiol., suppl. 27, pp. 61-70, 1969. [6] W. Gersch, "Spectral analysis of EEG's by autoregressive decomposition of time series," Mathematical Biosciences, vol. 7, pp. 205-222, 1970. [7] G. Pfurtscheller and S. Schuy, "Digital storage and simulation of EEG data using a linear EEG-model," Methods of Information in Medicine, vol. 14, pp. 80-86, Apr. 1975. [8] L. Zetterberg, "Estimation of parameters for a linear difference equation with application of EEG analysis," Mathematical Biosciences, vol. 5, pp. 227-275, 1969.
[9] A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York: McGraw-Hill, 1965. [10] G. E. P. Box and G. M. Jenkins, Time Series Analysis-Forecasting and Control. San Francisco: Holden-Day, 1970. [11] M. Kaveh and G. R. Cooper, "An empirical investigation of the properties of the autoregressive spectral estimator," IEEE Trans. Inform. Theory, vol. IT-22, pp. 313-323, May 1976. [12] D. Slepian, "Linear least-squares filtering of distorted images," J. Opt. Soc. oJ America, vol. 57, pp. 918-922, July 1967.
Reviews
Introduction to Digital Filtering-R. E. Bogner and A. G. Constantinides, Eds. (New York: Wiley-Interscience, 1975, 198 pp.). Reviewed by C. K. Yuen, University of Tasmania, Hobart, Tasmania, 7001. Only a few years ago, books on digital signal processing were appearing at the meagre rate of about one per year [1]-[6]. In the last couple of years publishers seemed to be rushing to correct the previous neglect: about ten books on the subject appeared in 1975 alone and a similar number since! With such fierce competition, a book will have to be very good indeed to do well, particularly in view of the high standard some of the books have set [7], [8]. The present volume is different from the others in that it is the joint
effort of eight contributing authors, all faculty members in electrical engineering departments at various English universities (though one has since moved to Australia), who, between them, produced eleven chapters. The coverage of the subject is fairly complete, although, constrained by the shortness of the book, many topics were only briefly mentioned. As the book is based on a "continuing education" course for practising engineers, the presentation is down to earth and clear. Also, the cost of the book is relatively low. Overall, the material in the book is sound engineering knowledge, and there is little that I would find fault with. If the book had appeared a year or two earlier I would have been happy to recommend it. Put against its competitors, however, the book must be judged to be less than the best. I believe most research workers will prefer Rabiner and Gold [7] as it contains more advanced and up-to-date material and covers all aspects of digital signal processing; whereas for teaching purposes Oppenheim and Schafer [8] would be better because it is, again, more complete in coverage and also contains exercises, a unique feature among the latest digital signal processing texts. A factor that reduces the usefulness of the present book as a reference is the lack of a good bibliography. The reference lists appended to the ends of the chapters are all quite short; and all together I counted only two citations later than 1972, both of work published in 1973. One paper, presented at a 1970 conference, was referred to in both Chapter 1 and Chapter 8, with the attached note: "probably in 1970 IEEE Trans. Audio Electroacou." Since the book is dated 1975, one wonders why somebody,
whether an editor, a contributing author, or an editorial assistant working for the publisher, did not look up the journal to verify if the paper actually was published. (It in fact appeared in the June 1970 issue of that journal.) Surely it is not too much to expect that authors should update their reference lists at the galley proof stage? This is neither time consuming nor excessively costly, and greatly helps the reader.
REFERENCES [1] B. Gold and C. M. Rader, Digital Processing of Signals. New York: McGraw-Hill, 1969. [2] J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures. New York: Wiley, 1971. [3] R. K. Otnes and L. Enochson, Digital Time Series Analysis. New York: Wiley, 1972. [4] G. M. Jenkins and D. G. Watts, Spectral Analysis and Its Applications. San Francisco: HoldenDay, 1968. [5] M. H. Ackroyd, Digital Filtering. London: Butterworths, 1973. [6] K. G. Beauchamp, Signal Processing. London: George Allen and Unwin, 1973. [7] L. R. Rabiner and B. Gold, Theory and Application oJ Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975. [8] A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: PrenticeHall, 1975.
Perturbation Methods-A. H. Nayfeh (New York: Wiley-Interscience, 1973, 415 pp.). Reviewed by Vimal Singh, Department of Electrical Engineering, Motilal Nehru Regional Engineering College, Allahabad 211004, India. There exist a number of approximate approaches for the analysis of nonlinear systems. Of these, the perturbation methods are the most commonly employed. Nayfeh's book is an excellent introduction to these
methods. In its seven chapters, the book presents notations, definitions, and the properties of asymptotic expansions (Chapter 1), the classification of the sources of nonuniformity in perturbation expansions (Chapter 2), the method of strained coordinates where uniformity is achieved by expanding the dependent as well as independent variables in terms of new independent parameters (Chapter 3), the methods of matched and composite asymptotic expansions (Chapter 4), variation of parameters and methods of averaging (Chapter 5), the methods of multiple scales (Chapter 6), and asymptotic solutions of linear ordinary and partial differential equations (Chapter 7). At the end of each chapter, about 20-30 exercises
418
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL.
are included. An exhaustive list of references appears at the end of the
book. The book is not concerned with the rigorous mathematical justifications of the techniques; rather, it describes the techniques as formal procedures and illustrates them by an ample number of examples. In preface, Nayfeh has rightly said that there are no rigorous mathematical justifications available yet for the expansions obtained for some of the complex examples treated in his book. It could as well be said that an approximate approach lacking complete justification may incidentally lead to an erroneous result. For instance, one of the three cases presented by R. N. Tiwari and R. Subramanian in a recent issue of the PROCEEDINGS OF THE IEEE, February 1977, p. 267, is false and hence, a counterexample to the two time scaling technique.
Applied Graph Theory: Graphs and Electrical Networks--W. K. Chen (New York: American Elsevier; and Amsterdam: North-Holland, 1976, 542 pp.). Reviewed by Chandra Satyanarayana, University of Alfateh, Tripoli, Libya. Graph theory, the prodigious child of Euler, continues to be increasingly used by the physical as well as the social sciences as reflected by the great number of published papers and books. The author, in his preface to the second revised edition of Applied Graph Theory, first published in 1971, observes that "The predictions are that it [graph theory and its applications] will continue to grow at a rapid rate for some time to come." The observation is well founded. The power of graph theory in providing insight in solving problems is once again demonstrated with the announcement [1] of a solution to the famous four-color problem by Appel and Haken in the Americani Mathetm?atical Society Biulletin. The announcement will surely trigger much discussion, retrospection, and reappraisal. The present edition of the book contains, in addition to the material of the first edition, a new chapter, "State Equations of Networks," and an updated bibliography. The first edition of the book provided a comprehensive treatment of applications of graph theory to electrical network theory, developed since the appearance of the classic book by Seshu and Reed [2]. In the second edition, besides state equations of networks, inclusion of additional topics of applications of graph theory to electrical network theory that are not found in the first edition (perhaps by pruning Chapters 3-5) would have enhanced the stature of the book. Topics that may have been incorporated are graph theory applications to network synthesis and solvability of active networks: these are consistent with the main theme of the book. Despite the few additions in the revised edition, the book has a wealth of material (some of which is the personal contribution of the author) presented with lucidity and rigor, interspersed with numerous examples to illustrate the concepts and brief historical backgrounds of the various topics. The book serves as an excellent reference text for further research and may also be adopted as a graduate text. The prerequisites of the book are minimal --introductory courses in network analysis and linear algebra would suffice. In addition to electrical engineers, the book may also be of interest to applied mathematicians and others interested in system modeling. The book has seven chapters. Chapters 1, 5, and 6 deal with graph theory, and the rest present applications of the theory to electrical network theory. Chapter 1 (pp. 1-35) introduces the terminology and basic concepts of graph theory. In Section 1.1., Introduction, the historical background on the four-color problem needs updating. Chapter 2 (pp. 36-139) presents foundations of electrical network theory using the concepts of graph theory. The chapter begins with a description of the circuit and cut matrices associated with a directed graph and their interrelationships, followed by a concise discussion of the vector spaces associated with them. The chapter provides a precise formulation of that network problem which deals with predicting the behavior of a network or a system of interconnected physical elements in terms of the characteristics of the elements and their manner of interconnection. The chapter includes the solution of the network problem by loop-and-cut methods, a thorough discussion of the invariance of the network functions with respect to the choice of circuits or cuts and incidence functions,
SMC-8, NO. 5,
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1978
Lunder which unique solutions can be obtained for the electrical networks. In Chapter 3 (pp. 140--223), applications of graph theory to the solutions of linear algebraic equations and to the eigenvalue problem hlave been presented in detail by considering both the associated Coates graph and the Mason graph. The thrust of Chapter 4 (pp. 24- 319) is to show how a network function may be written by inspection by consideiing the associated directed graph of the network. Chapter 5 (pp. 320-- 397) discusses properties of trees, thienl genieration. the existence of a Hamilton circvit, and the relationships between directed trees and directed Euler lines. Generation of trees by the Wang algebra formulation, decomposition without duplications, matrix formnulation, and elementary transformations have been presented, pointing lout the relative merits of each method of generation. Chapter 6 (pp 39S 463) presents necessary and sufficient conditions for the existence and iealization of a directed graph with prescribed degree pairs. Finally, in Chapter 7 (pp 464--517) the formulation of the explicit f'orm of state equations in normal form for a general linear network is presented. followed by a discussion of the physical meaning of the paranmeter matrices of the equation. The chapter concludes with a thoroLughi discussion of the order of complexity of a general linear time-inv ariant network. Inclusion of this chapter immediately after C'hapter 2 would havc Imaintained continuity of theme more effectively. The book has an impressive list of problems. some requiring roLutine applications of the text material and others requiring considerable extension. Overall, the book is extremely well written with the reader constantly in mind. and it may appeal to the novice as well as to the specialist. topological formulas for RLC networks, and conditions
REFERENCES [11
[2]
Time Magazitne New York. Sept. 20, 1976. S Seshu and M B. Reed, Linear Graph.s an1d Wesley 1961.
Elietrictl N7ctwoirkis Readinig MA A\ddison-
Systemanalyse, Systemplanung, Systemrealisierung, bei Prozessrechnerprojekten (System Analysis, System Planning, System Realization of Minicomputer Projects)-Rudiger Kaspers (Heidelberg: Alfred Hi-ithig, 1976, 148 pp.). Reviewed by George M. Siouris, Aerospace Guidance and Metrology Center, Newark
Air Force
Station, Newark, OH 43055.
When in 1971 the Intel Corporation came out with the first four-bit microcomputer, called the Intel 4004, the microcomputer revolution was under way. The microcomputer is a direct descendant of the minicomputer, the Digital Equipment Corporation's PDP-5 and PDP-8 which were introduced in 1963 and 1965, respectively. In particular, the PDP-8 became known as a minicomputer primarily because of its physical size, and not because of any limitations in its performance. Much of the success of the minicomputer industry was due to the dramatic advances in microelectronics since the early 1960's. Since the early 1960's, the rapid growth of the small digital computer has indeed revolutionized the process control
industry.
enormous amount of research effort that lhas been this area, the past few years have witnessed the debut of a phenomenal new electronic master-building block---the microprocessor, or as some workers in this field call it, computer on a few chips. Practically every major supplier of semiconductor devices is involved in the designl of digital logic devices, and new microprocessors are being announced each month. From the system designer's standpoint, the microprocessor has evolved from the architecture of the advanced minicomputers. Microprocessor manufacturers are using the easily available power of the microprocessor to increase automation in industrial equipment. Areas where planners are introducing minicomputers are 1) process contiol where computers are being used to direct as well as to monitor a particular process, 2) the machine tool industry, and 3) energy conservation where computers determine how and when energy should be used to name a few. Thus it is reasonable to expect that the explosive growth of microcomputer technology will continue. The present book is devoted to the planning and application of minicomputers in industrial process control automation. The book contains eight chapters. After some brief introductory remarks, Chapler 2 describes
As a result of the
going on
in
