Finite Difference Approximation

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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

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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Next: FDA in the Frequency Domain

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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