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Wave Digital Elements

When modeling mechanical systems composed of masses, springs, and dashpots, it is best to begin with an electrical equivalent circuit. Equivalent circuits make clear the network-theoretic structure of the system, clearly indicating, for example, whether interacting elements should be connected in series or parallel. Each element of the equivalent circuit can then be replaced by a first-order wave digital element, and the elements are finally parallel or series connected by means of scattering-junction interfaces known as adaptors.

Wave digital elements may be derived from their describing differential equations (in continuous time) as follows:

The next section will examine the above steps in greater detail.

An important benefit of introducing wave variables prior to bilinear transformation is the elimination of delay-free loops when connecting elementary building blocks. In other words, any number of elementary models can be interconnected, in series or in parallel, and the resulting finite-difference scheme remains explicit (free of delay-free loops).

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University