Nominal Design Guidelines

In general, we want

1. Subwoofer(s) up to $f_1$ Hz
2. VBAP from $f_1$ to $f_2$ Hz, or some simple stereo reduction
3. HOPs from $f_2$ to $f_3$ , where $f_3$ depends on listener age, etc.

Crossover frequency $f_1$ is normally set near the lower limit of stereo perception, which we are taking to be around 80 Hz (§2.12 on page ).

Crossover frequency $f_2$ is chosen to be the lowest frequency at which the lowest octave of the HOP is adequately sampled, following the analysis of §2 on page . For the five-band HOP example, it is $f_2=612$ Hz (§4.7 on page ). From a spatial sampling point of view, $f_2$ depends on listening geometry, particularly the stage-width, minimum-source-distance, and listener-distance from the array.

The setting for the upper limit $f_3$ can be based on how much high-frequency spatialization is desired. For older listeners,³¹ the top row is normally inaudible in arrays such as the previous example and in the five-band HOP examples above, such as Fig.13 on page . Therefore, the top row can either be simply omitted for older listeners, or, as a compromise preserving at least the presence of the high end for the occasional younger listener, replaced by conventional stereo tweeters (two-channel VBAP), or any number of tweeters in an undersampled VBAP row, or coaxial mounts along any lower row. Also, at such high frequencies, wavelengths are so small that left-right processing is noncoherent, so that left-or-right ``presence'' is the only available cue for perception. Thus, an undersampled top row should work quite well for those who can hear it at all. Finally, much auditory direction perception research ignores frequencies above 10 kHz.