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System Block Diagram

A schematic diagram of a stereo multiple-source simulation is shown in Fig.[*]. To simplify the layout, the input and output signals are all on the right in the diagram. For further simplicity, only one input source is shown. Additional input sources are handled identically, summing into the same delay lines in the same way.

Figure 2: Block diagram of a stereo simulator for any number of moving sound sources.

The input source signal first passes through filter $ H_0(z)$ , which provides time-invariant filtering common to all propagation paths. The left- and right-channel filters $ H^{(n)}_{0L}(z)$ and $ H^{(n)}_{0R}(z)$ are typically low-order, linear, time-varying filters implementing the time-varying characteristics of the shortest (time-varying) propagation path from the source to each listener. (The $ (n)$ superscript here indicates a time-varying filter.) These filter outputs sum into the delay lines at arbitrary (time-varying) locations using interpolating writes (de-interpolation). The zero signals entering each delay line on the left can be omitted if the left-most filter overwrites delay memory instead of summing into it.

The outputs of $ H^{(n)}_{0L}(z)$ and $ H^{(n)}_{0R}(z)$ in Fig.[*] correspond to the ``direct signal'' from the moving source, when a direct signal exists. These filters may incorporate modulation of losses due to the changing propagation distance from the moving source to each listener, and they may include dynamic equalization corresponding to the changing radiation strength in different directions from the moving (and possibly turning) source toward each listener.

The next trio of filters in Fig.[*], $ H_1(z)$ , $ H^{(n)}_{1L}(z)$ , and $ H^{(n)}_{1R}(z)$ , correspond to the next-to-shortest acoustic propagation path, typically the ``first reflection,'' such as from a wall close to the source. Since a reflection path is longer than the direct path, and since a reflection itself can attenuate (or scatter) an incident sound ray, there is generally more filtering required relative to the direct signal. This additional filtering can be decomposed into its fixed component $ H_1(z)$ and time-varying components $ H^{(n)}_{1L}(z)$ and $ H^{(n)}_{1R}(z)$ .

Note that acceptable results may be obtained without implementing all of the filters indicated in Fig.[*]. Furthermore, it can be convenient to incorporate $ H_i(z)$ into $ H^{(n)}_{iL}(z)$ and $ H^{(n)}_{iR}(z)$ when doing so does not increase their orders significantly.

Note also that the source-filters $ H^{(n)}_{iL}(z)$ and $ H^{(n)}_{iR}(z)$ may include HRTF filtering [2,19] in order to impart illusory angles of arrival in 3D space.

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``Doppler Simulation and the Leslie'', by Julius O. Smith III, Stefania Serafin, Jonathan Abel, David P. Berners, Music 421 Handout, Spring 2002 .
Copyright © 2016-03-26 by Julius O. Smith III, Stefania Serafin, Jonathan Abel, David P. Berners
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University