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

[Julius Smith]

Hi All - I agree with your reasonings that temporal spacings and decay
times should be preserved as much as possible.  Cheers - Julius

On Mon, Jun 26, 2017 at 3:16 PM, Perry Cook <prc at cs.princeton.edu> wrote:

> Great question.  In the case of all pass filters, I at first felt your
> intuition correct.
>
> But as I think of it, maybe not.  My reasoning:
>
> I’ve most often used all pass with large delay line for reverb and other
> delay
> effects.  (Schroeder type) Reverbs usually use some comb filters and some
> all pass.  I always view these delays as round-trip times between simulated
> walls.  So the time is important, thus the delay length (as a number of
> samples)
> must change with sample rate, to keep the time delay the same.
>
> For the comb filters, the decay time is important, so the coefficient
> needs to
> change with sample rate to keep the T60 correct.
>
> For the all-pass filters, maybe we should change them as well, to keep the
> transient response more constant across different sample rates.  An all
> pass
> shows up as reciprocal pairs of poles/zeros spaced around the unit circle.
> Changing the delay line length changes the number and positions of those,
> but they always equally divide the unit circle.  One could posit different
> arguments that the distance(s) from the unit circle should or should not
> change.
>
> One argument:   product of all pole radii = constant      (keep
> coefficient same)
>
> Other argument: individual pole radii = constant   (change coefficient)
>
>
> Julius specifically called to pipe in here
>
> PRC
>
>
> > On Jun 25, 2017, at 9:02 AM, Gary Worsham <gary.worsham at gmail.com>
> wrote:
> >
> > 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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>
>
>
>


-- 

Julius O. Smith III <jos at ccrma.stanford.edu>
Professor of Music and, by courtesy, Electrical Engineering
CCRMA, Stanford University
http://ccrma.stanford.edu/~jos/ <http://ccrma.stanford.edu/>
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