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_{sl}/c$ corresponds source motion toward the listener at speed $ v_{sl}$. When this is done, we must use interpolating writes into the delay memory. Interpolating writes may be called de-interpolation [502], and they are formally the graph-theoretic transpose of interpolating reads (ordinary ``interpolation'') [333]. A review of time-varying, interpolating, delay-line reads and writes, together with a method using a single shared pointer, are given in [383].

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Vector Formulation