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Wave Digital Filter (WDF) Construction

Wave digital elements may be derived from their describing differential equations (in continuous time) as follows:

  1. Express forces and velocities as sums of traveling-wave components (``wave variables''):

    \begin{eqnarray*}
f(t) &=& f^{{+}}(t)+f^{{-}}(t)\\
v(t) &=& v^{+}(t)+v^{-}(t)
\end{eqnarray*}

    The actual ``travel time'' is always zero.
    (For historical reasons, WDFs typically use traveling-wave components scaled by 2.)

  2. Digitize via the bilinear transform (trapezoid rule)

  3. Use scattering junctions (``adaptors'') to connect elements together in


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Download WaveDigitalFilters.pdf
Download WaveDigitalFilters_2up.pdf
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``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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