Multiple Write Pointers

It is interesting to consider also what effects can be achieved using multiple de-interpolating write pointers. From the considerations in §3.4.5, we see that multiple write-pointers correspond to multiple write-heads on a magnetic tape recorder. If they are arranged at a fixed spacing, they are equivalent to multiple read pointers, providing a basic multipath simulation. If, however, the write pointers are moving independently, they induce independent Doppler shifts due to source motion. In particular, each write-pointer can lay down a signal from a separate source to a single listener with its own Doppler shift. Furthermore, each write-signal can be passed through its own filter. Such an individualized source filter can implement all filtering incurred along the propagation path from each source to the listener.

When all write pointers have the same input signal, their filters can be implemented using a series chain in which the outputs of successive filters in the chain correspond to progressively longer propagation paths (progressively more filtering). Such an implementation can greatly reduce the filter order required for propagation paths longer than the shortest.

The write-pointers may cross each other with no ill effects, since all but the first^4.5 simply sum into the shared delay line.

We have seen that a single delay line can be used to simulate any number of moving listeners (§3.4.5) or any number of moving sources. However, when simulating both multiple listeners and multiple sources, it is not possible to share a single delay line. This is because the different listeners do not see the same Doppler shift for each moving source, and while the listener's read-pointer motion can be adjusted to correct for the Doppler shift seen from any particular source, it cannot correct for more than one in general. Thus, in general, we need as many delay lines as there are sources or listeners, whichever is smaller. More precisely, if there are moving sources and moving listeners, simulation requires delay lines.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.