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Mathematics



Book Title : Physical Audio Signal Processing
eBook download format(s) : htm
Author(s) : Julius O. Smith III
Section : Mathematics
Book Review:

Book Description
This book was developed for my course entitled "Signal Processing Methods in Musical Acoustics," which I have given at the Center for Computer Research in Music and Acoustics (CCRMA) every year since 1984. The course was created primarily as a research preparation and dissemination vehicle intended for graduate students in computer music and engineering interested in efficient computational modeling of musical instruments. Ideally, in addition to a first course in digital signal processing [454,453], the student will also have studied elementary physics, including waves, and a prior first course in acoustics is desirable.

The Web version of this book contains hypertext links to more elementary material, thus rendering it significantly more self contained. The availability of the Web while writing this book greatly influenced its construction. In particular, the main chapters attempt to get immediately "down to business," skipping typical "preliminaries." The intent is that the reader will follow links as needed to fill in prerequisite concepts. While following links is of course far quicker on the Web, a large collection of appendices has been provided to make the physical book reasonably self contained as well.

The driving goal behind the research and course leading to this book is the development of "virtual musical instruments" and audio effects in the form of efficient algorithms suitable for real-time execution on general purpose computers. Technically, the first area can be described as "signal processing models of physical models of musical instruments." That is, the starting point is typically a mathematical model of a musical instrument from the field of musical acoustics, and the final algorithms are expressed as computational forms from the field of signal processing. In the realm of computational physics, this book might be described as being focused on "real-time finite-difference schemes" for modeling the behavior of acoustic systems.

In one sense, this book is about how to avoid the computational expense associated with using general purpose differential equation solvers, such as finite difference schemes, applied in a "brute force" way. In other respects, it is about the art of homing in on the "essential ingredients" of an acoustic instrument and taking advantage of "data reduction" inherent in human hearing in order to minimize computational expense. In the early days of computer music, it was not uncommon to run "acoustic compilers" orders of magnitude slower than real time to compute sound. Nowadays, computers are so fast that physical modeling synthesis can be (and is) integrated in software synthesizers running on inexpensive personal computers without special synthesizer hardware. However, to obtain the best results on a given machine, it is still necessary to simplify computational complexity relative to more general numerical simulation techniques.

As indicated in the foregoing, the material of this book is multidisciplinary, building on results from physics, musical acoustics, psychoacoustics, signal processing, control engineering, computer music, and computer science. Such diversity is typical of applied research.

For the composer interested in using the models for musical sound synthesis, it is fine to skip over anything not understood on first reading, such as transfer functions and use of Fourier theorems. An attempt has been made to keep high-level theory as concise, unobtrusive, and bottom-line oriented as possible, with detailed coverage deferred to the appendices. In the Web version, most technical terms are linked to associated tutorials. Most software-related information appears in the first few appendices, although there are snippets of software distributed throughout the text as well. All software is freely available, and the quickest way to grab something is probably via copy/paste from the Web version.




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