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Wave Digital Filters

Wave digital elements may be derived 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.

  2. Digitize via the bilinear transform (trapezoid rule)

  3. Use scattering junctions (``adaptors'') to connect elements together in series and/or parallel.


Subsections
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Download SMAC03S.pdf
Download SMAC03S_2up.pdf
``Recent Developments in Musical Sound Synthesis Based on a Physical Model'', by Julius O. Smith III, (Stockholm Musical Acoustics Conference (SMAC-03), August 6--9, 2003).
Copyright © 2006-02-19 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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