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

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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