This book was developed for my course entitled ``Signal Processing Models 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 [454,452], 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 more self contained.

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 or embedded processors. As a result, the emphasis is on ``signal processing models of physical models'' of musical instruments and audio effects. The starting point is typically a mathematical model of a musical instrument from the field of musical acoustics, or a circuit description of an audio effect, and the final algorithms are expressed as computational forms from the field of signal processing. In the realm of computational physics, such algorithms might be called ``real-time finite-difference/solution-propagation schemes''.

In one sense, this book is about how to avoid the computational expense associated with using general purpose differential equation solvers, such as most 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.

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