[Stk] tuning all pass filters with changes in sampling rate

[Gary Worsham]

Single pole IIR filters can easily be adjusted to a new sampling rate while
preserving frequency response since the coefficient includes the sampling
rate as part of its formula.

However, in sound effects use (my experience anyway) all pass filters are
used for phase shifter (e.g. Pink Floyd) and as a component in most
reverbs.  These structures tend to be more ad-hoc in their design intention
- by which I mean that after a bit of experience, most people would know
what to expect from an 800 Hz low pass vs. a 2.5 kHz low pass, but as far
as what to expect from these other things, I think mostly we just wing it
and see what happens.

All-pass tuning (frequency of max phase shift) is related to the length of
the all-pass delay, and for delays longer than one sample, this shift is
mirrored and copied throughout the spectrum.  So I can adjust the all-pass
delay sample length proportionally with the ratio of new/old sample rate
and it should preserve the delay time.

Next question is about the all-pass coefficient.  Generally I think "how
often does the signal go through the coefficient"?  If you adjust the delay
length to equalize the time, then my gut feeling is to keep the all-pass
coefficients the same regardless of sampling rate.

However that is simply a wild guess, so thought I'd check in the the DSP
gods.

Thanks,

GW
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