- Conservation of Mass:

- Conservation of Momentum:

Now, let us rename density by a variable , and momentum density by a variable , which we will associate with currents:

and finally:

Now each or applied to a ``current'' such as or might be thought of as some sort of voltage corresponding to a generalized inductor (i.e., temporal or spatial). This is merely a way of making the jump to the following circuit representation of the equations:

- After a coordinate change, and impedance transformations (to remove negative inductances), we are left with a circuit that can be
*discretized*according to WDF principles outlined above. - MD-WDF one-ports are simple generalizations of their 1-D equivalents, except that internal delays may include spatial steps as well.
- Scattering is still memoryless (KCL equations depend only on voltage and current, not on the independent variuables).

Download WaveDigitalFilters.pdf

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Download WaveDigitalFilters_4up.pdf

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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