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Doppler Simulation via Delay Lines

Figure 5.5: Delay line with variable read-pointers and write-pointers.

This analogy also works for a delay-line based computational model, as depicted in Fig.5.5. The magnetic tape is now the delay line, the tape read-head is the read-pointer of the delay line, and the write-head is the delay-line write-pointer. In this analogy, it is readily verified that modulating delay by changing the read-pointer increment from 1 to $ 1+v_{ls}/c$ (thereby requiring interpolated reads) corresponds to listener motion away from the source at speed $ v_{ls}$ . It also follows that changing the write-pointer increment from $ 1$ to $ 1+v_{s,l}/c$ corresponds source motion toward the listener at speed $ v_{s,l}$ . When this is done, we must use interpolating writes into the delay memory. Interpolating writes may be called de-interpolation [506], and they are formally the graph-theoretic transpose of interpolating reads (ordinary ``interpolation'') [336]. A review of time-varying, interpolating, delay-line reads and writes, together with a method using a single shared pointer, are given in [386].

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University