BOOK REVIEWS

James F. Bartram 94 Kane Avenue, Middletown, Rhode Island 02840

The opinions expressed are those of the individual reviewers and are not necessar//y endorsed by the Ed/toria/ Board of this Journa/.

Editorial Policy:/f there is a negative review, the author of the book w/i/be given a chance to respond to the review/n this section of the Journa/ and the reviewer w/i/be a//owed to respond to the author's comments. [See "Book Reviews Editor's Note, "J. Acoust. Soc. Am. 81, 1651 (May 1987).]

Mecanique des Milieux Poreux Olivier Coussy

Editions Technip, Paris, France, 1991. xxi 4- 43 7 pp. Price 495francs. ISBN: 2- 7108-0595-2.

Mechanics of porous media is a hybrid science, drawing on various disciplines: elasticity, plasticity, fluid mechanics, and thermodynamics. The theory of porous solids is fundamental to geophysics and soil mechan- ics. It is relevant to engineering applications of major economic importance, in particular to the extraction of oil.

In spite of the pivotal importance of this branch of applied mechanics, this reviewer is only aware of contributions to the periodical literature, such as the sequence of classical papers by M. A. Blot. To this reviewer's knowl- edge, Olivier Coussy's work is the first endeavor at consolidating the theory of the mechanics of porous media in a comprehensive book. The author is a member of the faculties of the two most prestigious engineering schools of France. To an American audience, his other title (Research Engineer at the Central Laboratory for Bridges and Highways) sounds surprisingly practi- cal for a researcher who is primarily a superb theoretician.

Coussy's work is eminently satisfying. It is self-contained, the system- atic development starting from fundamental concepts of mechanics of solid media and extending to all significant ramifications of the theory, viz., to situations as complex as a porous solid whose communicating interstices contain a gas and a fluid in the form of liquid or vapor. The book is purely theoretical, no practical applications being covered. It is accessible to an audience of applied physicists and graduate engineers with no previous ex- perience in this discipline but with a taste for mathematical rigor. Since the technical and scientific audience in the United States appears to become increasingly monolingual, second language requirements not withstanding, the reviewer hopes that this important book will be translated.

MIGUEL C. JUNGER

Cambridge Acoustical Associates, Inc. 80 Sherman Street

Cambridge, Massachusetts 02140

Digital Signal Processing---Efficient Convolution and Fourier Transform Techniques

D.G. Myers Prentice-Hall, New York, NE 1990.

xi 4- 355pp.

Digital signal processing (DSP) has become an important tool in a variety of applications such as sonar, radar, acoustics, biomedical engineer- ing, and many others. DSP deals with representation of signals by sequences of numbers and processing of these number sequences. The objective of such processing may be, for example, to estimate parameters of a signal or to transform signals into a form which in some sense is more desirable or more easily understood. High-speed digital computer technology has fostered the development of sophisticated signal processing algorithms for applications in many fields such as sonar, radar, and medical engineering.

This book, Digital Signal Processing--Efficient Convolution and Four- ier Transform Techniques, focuses purely on convolution aspects of digital signal processing. It is concerned purely with the mechanics of digital con- volution, and addresses various efficient methods of digital convolution, which is at the core of digital signal processing. Convolution arises when an input signal is provided to a mathematical model in order to produce an output signal. This book focuses on two approaches to convolution. One, the direct approach, focuses on the equations themselves; and the second transforms the problem into frequency domain where convolution is easier.

This book is intended mainly for senior undergraduates and beginning graduate students; in particular, students in engineering, geology, physics, mathematics, computer science, and similar disciplines seeking a knowl- edge of advanced signal processing methods. This is an unusual book, both in terms of organization of material and approaches leading to the solution of a problem.

This book has four parts. The first sets the framework for the endeavor and reviews and introduces some general mathematical results. The second concentrates on the various fast Fourier transform techniques together with some related methods. The third looks at a number of theoretic approaches to digital convolution. The fourth looks at polynomials.

The more unusual aspects of the format lie within the parts themselves. Except for Part 1, the other parts consist mainly of tools, theory, develop- ments and implementation issues. The initial emphasis is on tools--math- ematical techniques which can be employed, followed by theory--the work- ing base of knowledge created with the tools and aimed at a broad spectrum of applications. Finally, implementation issues are considered--the practi- cal concerns of engineering solutions.

Part 1 deals with problem foundations, including the application of digital convolution in the area of sonar, radar, medical engineering, con- cepts of digital convolution, the algorithms of digital convolution, exercises and problems, and mathematical foundations.

The heart of the book is digital convolution. Therefore, a few images of digital convolution [for example, Figs. 3.5 through 3.13 (Ref. 1 ) ] are help- ful in understanding digital convolution from abstract concepts. The sec- tioned convolution, as shown in Fig. 1.2, is not sufficient. The figure axes concerning overlap and add/save need to be labeled. This would permit the students to actually self execute and fully understand each method. Some image of the Fourier transform compared to DFT would provide a better comprehension of its origins. The example in the Tom-Cook algorithm is clear, and breaking it down in stages is a good idea.

Part 2 is devoted exclusively to the study of fast Fourier transform, but also examines improved techniques of the discrete Fourier technique (DFT). Most of these techniques are characterized by combination proce- dures for constructing long-length from short-length DFTs.

Part 3 begins with an examination of number theory and with the properties of numbers. The Raders theorem (in the tool section) is exam- ined. This theorem shows that in certain circumstances the DFT and convo-

lution are very closely related. The development section begins by examin- ing a simple application of number theory that deals with the prime factor algorithm. The body of this section is an examination of various number- theoretic transforms. These have some attraction for hardware implemen- tations.

Part 4 looks at the polynomial congruence and related matters. Three topics are examined, that include Winograd's minimal complexity algo- rithm, minimal multiplication algorithm, and polynomial transforms. The applications of Winograd's theorem and the Chinese remainder theorem are closely investigated. The Winograd's theorem offers a powerful means

536 J. Acoust. Soc. Am. 91 (1), January 1992 0001-4966/92/010536-03500.80 ¸ 1992 Acoustical Society of America 536

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