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Finite Difference Approximation

A finite difference approximation (FDA) approximates derivatives with finite differences, i.e.,

$\displaystyle \frac{d}{dt} x(t) \isdefs \lim_{\delta\to 0} \frac{x(t) - x(t-\delta)}{\delta} \;\approx\; \frac{x(n T)-x[(n-1)T]}{T} \protect$ (8.2)

for sufficiently small $ T$ .8.5

Equation (7.2) is also known as the backward difference approximation of differentiation.

See §C.2.1 for a discussion of using the FDA to model ideal vibrating strings.



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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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