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Algebraic Derivation


\epsfig{file=eps/pise.eps,width=6in}

By inspection:

$\displaystyle F_o(z) = z^{-N} \left\{ F_i(z) + z^{-2M}\left[F_i(z) + z^{-N} H_l(z)F_o(z)\right]\right\}
$

\begin{eqnarray*}
\Rightarrow\quad
H(z) \mathrel{\stackrel{\Delta}{=}}\frac{F_o(...
...}}\\
&=& \left(1+z^{-2M}\right)\frac{z^{-N}}{1-z^{-(2M+2N)}}\\
\end{eqnarray*}

\epsfig{file=eps/pianoSimplifiedISEExtracted.eps,width=6in}


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``Elementary Digital Waveguide Models for Vibrating Strings'', by Julius O. Smith III and Nelson Lee,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Julius O. Smith III and Nelson Lee
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA