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Physical Audio Signal Processing
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Semi-Implicit Backward Euler
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Semi-Implicit Backward Euler
The semi-implicit backward Euler method is defined by [555]
![$\displaystyle \underline{\hat{x}}(n) \isdefs \underline{\hat{x}}(n-1) + T\, \frac{f[n,\underline{\hat{x}}(n-1)]}{1-T\,\ddot{\underline{\hat{x}}}(n-1)} \protect$](http://www.dsprelated.com/josimages_new/pasp/img1725.png)
where
denotes an estimate of the second time
derivative
.
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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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