Introduction to Digital Filtering

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