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Reviewer: Vladimir Botchev

In the past, most of the material on sound synthesis through physical modeling was only available through academic reports, conference papers, and journal publications. Although a similar title was published fairly recently [1], there was still a need for a systematic tutorial that presented advanced techniques, which this unique book on audio engineering fulfills to perfection. A very strong feature of the book is its down-to-earth explanation of complex concepts and its practical derivations of useful solutions. Indeed, partial differential equations (PDEs) are hardly in extensive everyday use by most audio engineers, but they are unavoidable in the type of sound synthesis that this book is concerned with. The fact that the author manages to facilitate the understanding of these and other similar topics is quite a feat in itself. Rather than summarizing the material by its table of contents, this review favors a more general account of the book's content that will be more informative for a broader audience. Bilbao starts by providing some background material in sound synthesis and a brief historical account of how the field has evolved. He then continues with further background on mathematical operations, which, while familiar to a signal processing practitioner, are cast into the framework of ordinary differential equations (ODEs) and PDEs. The thorough analysis of oscillators, a crucial component for physical synthesis, comes next. Next, a substantial body of text is devoted to the one-dimensional (1D) wave equation and the various physical models that can be derived with it, including linear and nonlinear effects. Typical musical devices are analyzed with regard to physical synthesis, such as strings, bars, bows, coupling of hammers with strings and bars, and helical springs, including an interesting discussion on spring reverberation. This so-to-speak 1D detailed presentation ends with a chapter that introduces acoustic instrument synthesis, such as woodwind, brass, and even speech synthesis. Continuing further, at the same level of detail, the book presents a two-dimensional (2D) extension of the 1D discussion. Starting with a presentation of the basic mathematical tools needed for the 2D case, this last part of the book continues with 2D wave equation analysis and plate-vibration-based synthesis details, including many details on plate reverberation (which are sufficient enough to actually build such a device model). This part ends with material on how to simulate percussion effects. The author's supplemental Web site (http://www2.ph.ed.ac.uk/~sbilbao/nss.html) provides several sound examples, including MATLAB codes (also listed in the appendix) that implement various modeling procedures-for example, a functioning model of a plate reverberation requires little effort and tuning in order to be transposed on a real-time platform. In conclusion, I highly recommend this book as an introduction to the field of physical modeling for sound synthesis, which is becoming more and more popular with the tremendous increase in affordable computer power, through multicore desktops and laptops and supercomputer-like graphics processing unit (GPU) engines. Online Computing Reviews Service