<div dir="ltr">Hi All - I agree with your reasonings that temporal spacings and decay times should be preserved as much as possible. Cheers - Julius</div><div class="gmail_extra"><br><div class="gmail_quote">On Mon, Jun 26, 2017 at 3:16 PM, Perry Cook <span dir="ltr"><<a href="mailto:prc@cs.princeton.edu" target="_blank">prc@cs.princeton.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Great question. In the case of all pass filters, I at first felt your intuition correct.<br>
<br>
But as I think of it, maybe not. My reasoning:<br>
<br>
I’ve most often used all pass with large delay line for reverb and other delay<br>
effects. (Schroeder type) Reverbs usually use some comb filters and some<br>
all pass. I always view these delays as round-trip times between simulated<br>
walls. So the time is important, thus the delay length (as a number of samples)<br>
must change with sample rate, to keep the time delay the same.<br>
<br>
For the comb filters, the decay time is important, so the coefficient needs to<br>
change with sample rate to keep the T60 correct.<br>
<br>
For the all-pass filters, maybe we should change them as well, to keep the<br>
transient response more constant across different sample rates. An all pass<br>
shows up as reciprocal pairs of poles/zeros spaced around the unit circle.<br>
Changing the delay line length changes the number and positions of those,<br>
but they always equally divide the unit circle. One could posit different<br>
arguments that the distance(s) from the unit circle should or should not change.<br>
<br>
One argument: product of all pole radii = constant (keep coefficient same)<br>
<br>
Other argument: individual pole radii = constant (change coefficient)<br>
<br>
<br>
Julius specifically called to pipe in here<br>
<br>
PRC<br>
<div><div class="h5"><br>
<br>
> On Jun 25, 2017, at 9:02 AM, Gary Worsham <<a href="mailto:gary.worsham@gmail.com">gary.worsham@gmail.com</a>> wrote:<br>
><br>
> 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.<br>
><br>
> 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.<br>
><br>
> 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.<br>
><br>
> 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.<br>
><br>
> However that is simply a wild guess, so thought I'd check in the the DSP gods.<br>
><br>
> Thanks,<br>
><br>
> GW<br>
><br>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div>
<p>Julius O. Smith III <<a href="mailto:jos@ccrma.stanford.edu" target="_blank">jos@ccrma.stanford.edu</a>><br>
Professor of Music and, by courtesy, Electrical Engineering<br>
CCRMA, Stanford University<br>
<a href="http://ccrma.stanford.edu/" target="_blank"><span>http://ccrma.stanford.edu/~jos/</span></a> </p></div></div></div>
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