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Piano String Finite Difference Scheme

The Chaigne and Askenfelt PDE is discretized in space and time to yield a recursive difference scheme with the following space-time ``stencil'':

\epsfbox{eps/depend.eps}

The FDS can be written in matrix form as

\begin{eqnarray*}
{\bf y}_{n} ={\bf A_{1}y_{n-1}}+{\bf A_{2}y_{n-2}}+{\bf A_{3}y_{n-3}}+{\bf g}f_n({\bf y}_{n-1}[i_h],y^h_{n-1})
\end{eqnarray*}

where



Subsections
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Download PianoString.pdf
Download PianoString_2up.pdf
Download PianoString_4up.pdf

``Modal Synthesis of a Piano String'', by Stefan Bilbao and Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2019-02-05 by Stefan Bilbao and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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