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Interpretation of the Time-Domain KW Converter

As shown above, driving a single displacement sample $ y_{n,m}$ in the FDTD corresponds to driving a velocity input at position $ m$ on two alternating subgrids over time. Therefore, the filter $ H(z)=1-z^{-2}$ acts as the filter $ H(z)=1-z^{-1}$ on either subgrid alone--a first-order difference. Since displacement is being simulated, velocity inputs must be numerically integrated. The first-order difference can be seen as canceling this integration, thereby converting a velocity input to a displacement input, as in Eq.$ \,$ (E.23).


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA