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Expanded Wave Digital Spring-Mass System

\begin{center}
\epsfig{file=eps/wallspringmasswdfexp.eps,width=\textwidth } \\
State variables labeled $x_1(n)$\ and $x_2(n)$
\end{center}

Low-Frequency Analysis:

The reflection coefficient for our parallel force-wave connection is given as usual by the impedance step over the impedance sum:

$\displaystyle s= \frac{mc - k/c}{mc + k/c}
= \frac{m2/T - kT/2}{m2/T + kT/2}
= \frac{m - kT^2/4}{m + kT^2/4} \approx 1
$

We can now see what's going physically at low frequencies relative to the sampling rate:


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Download WaveDigitalFilters.pdf
Download WaveDigitalFilters_2up.pdf
Download WaveDigitalFilters_4up.pdf

``Wave Digital Filters'', by Stefan Bilbao and Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2017-06-05 by Stefan Bilbao and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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