[sdiy] Multi-output comb filter?

Tue May 22 12:00:29 CEST 2018

So what I thought might be feasible would be to eg get a single peak at 1
Hz, create a 1 Hz comb filter, then subtract a 2 Hz comb from it so you're
left with peaks at 1, 3, 5, 7, etc Hz, then subtract a 3 Hz comb, so you're
left with 1, 5, -6, 7, 9, 11, -12, etc Hz, then subtract a 5 Hz comb etc.
If you look at the first 249 such filters (that's what I could quickly
calculate), you will get these coefficients:

+--0-+-00+-0-++0-0-0++
-00+00---0+++0-++0---0
0+-000+0-0+0++-0-+00+-
-0+--0-+00+--00+-0+++0
-0+0+++0-000---0-+-0--
+0--+00++00++000-0+--0
++00---0+++0++00-0-00-
+0-++0+0-0-+-00-00--00
++-0--+0+-+00--0-+-0-0
-0+++0++00++-0+++0+++0
+--00+-0---0-0+0+--0-0
000-+0

Meaning: 1 * comb at 1 Hz, -1 * comb at 2 Hz, -1 * comb at 3 Hz, 0 * comb
at 4 Hz, -1 * comb at 5 Hz, 1 * comb at 6 Hz, etc.

I assume this can be found for each nth peak, and a lot of the data will be
shared. Note you still need (nyquist/f) delays with 1 bucket, 2 buckets,
..., nyquist buckets. That's a good 468 megabytes at a 44.1 kHz sampling
frequency. I wonder if this too can be shared somehow.

I don't really see a pattern to the coefficients - i used a program to find
them - does anyone else see any rule?

The program can be found here:
https://lpaste.net/6557071818560110592

You have to use the deepseq package.
Change endHz to 250 and run firstPeakOnly from the repl. I'm not sure if
the last coeff will be the same as with 22050, as I haven't calculated it
up to that number, and I don't really have time to optimize this any more.

On Tue, 22 May 2018 07:37 , <rsdio at audiobanshee.com> wrote:

> On May 21, 2018, at 10:04 PM, Corey K <coreyker at gmail.com> wrote:
> >   Option 2: write out the Z-transform for your comb filter. There will be
> >   one pole per peak, and these will be spaced at equal angles around a
> >   circle in the complex place. Add a zero to perfectly cancel the pole
> >   corresponding to the peak you want removed. This will in turn
> >   correspond to an FIR filter that you can run before or after your comb
> >   filter.
>
> Hereâ€™s an exercise that might prove interesting:
>
> Write out the Z-transform for an ideal comb filter. Then convert this to
> an FIR filter without any modification.
>
> My question is this: Is the math perfect enough that youâ€™d end up with a
> single delay tap? I mean, thatâ€™s what a comb filter is, so I wonder whether
> the Z-transform to FIR would actually guide you to the simplest
> implementation. Granted, the FIR would probably be equivalent to a string
> of individual Z-1 delays, but theyâ€™re equivalent to a single, long delay so
> long as nothing taps the intermediate samples.
>
> I have a suspicion that things wouldnâ€™t quite work out so perfectly, and
> thereâ€™s be lots of taps, each with their own weight, and it wouldnâ€™t come
> out looking like the simple single-delay-plus-mixer circuit.
>
> Has anyone gone through the exercise to see how it turns out?
>
> Brian
>
>
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at synth-diy.org
> http://synth-diy.org/mailman/listinfo/synth-diy
>
-------------- next part --------------
   So what I thought might be feasible would be to eg get a single peak at
   1 Hz, create a 1 Hz comb filter, then subtract a 2 Hz comb from it so
   you're left with peaks at 1, 3, 5, 7, etc Hz, then subtract a 3 Hz
   comb, so you're left with 1, 5, -6, 7, 9, 11, -12, etc Hz, then
   subtract a 5 Hz comb etc. If you look at the first 249 such filters
   (that's what I could quickly calculate), you will get these
   coefficients:

   +--0-+-00+-0-++0-0-0++
   -00+00---0+++0-++0---0
   0+-000+0-0+0++-0-+00+-
   -0+--0-+00+--00+-0+++0
   -0+0+++0-000---0-+-0--
   +0--+00++00++000-0+--0
   ++00---0+++0++00-0-00-
   +0-++0+0-0-+-00-00--00
   ++-0--+0+-+00--0-+-0-0
   -0+++0++00++-0+++0+++0
   +--00+-0---0-0+0+--0-0
   000-+0

   Meaning: 1 * comb at 1 Hz, -1 * comb at 2 Hz, -1 * comb at 3 Hz, 0 *
   comb at 4 Hz, -1 * comb at 5 Hz, 1 * comb at 6 Hz, etc.

   I assume this can be found for each nth peak, and a lot of the data
   will be shared. Note you still need (nyquist/f) delays with 1 bucket, 2
   buckets, ..., nyquist buckets. That's a good 468 megabytes at a 44.1
   kHz sampling frequency. I wonder if this too can be shared somehow.

   I don't really see a pattern to the coefficients - i used a program to
   find them - does anyone else see any rule?

   The program can be found here:
   [1]https://lpaste.net/6557071818560110592

   You have to use the deepseq package.
   Change endHz to 250 and run firstPeakOnly from the repl. I'm not sure
   if the last coeff will be the same as with 22050, as I haven't
   calculated it up to that number, and I don't really have time to
   optimize this any more.

   On Tue, 22 May 2018 07:37 , <[2]rsdio at audiobanshee.com> wrote:

     On May 21, 2018, at 10:04 PM, Corey K <[3]coreyker at gmail.com> wrote:
     >Â  Â Option 2: write out the Z-transform for your comb filter.
     There will be
     >Â  Â one pole per peak, and these will be spaced at equal angles
     around a
     >Â  Â circle in the complex place. Add a zero to perfectly cancel
     the pole
     >Â  Â corresponding to the peak you want removed. This will in turn
     >Â  Â correspond to an FIR filter that you can run before or after
     your comb
     >Â  Â filter.
     Hereâs an exercise that might prove interesting:
     Write out the Z-transform for an ideal comb filter. Then convert
     this to an FIR filter without any modification.
     My question is this: Is the math perfect enough that youâd end up
     with a single delay tap? I mean, thatâs what a comb filter is, so I
     wonder whether the Z-transform to FIR would actually guide you to
     the simplest implementation. Granted, the FIR would probably be
     equivalent to a string of individual Z-1 delays, but theyâre
     equivalent to a single, long delay so long as nothing taps the
     intermediate samples.
     I have a suspicion that things wouldnât quite work out so perfectly,
     and thereâs be lots of taps, each with their own weight, and it
     wouldnât come out looking like the simple single-delay-plus-mixer
     circuit.
     Has anyone gone through the exercise to see how it turns out?
     Brian
     _______________________________________________
     Synth-diy mailing list
     [4]Synth-diy at synth-diy.org
     [5]http://synth-diy.org/mailman/listinfo/synth-diy

References

   1. https://lpaste.net/6557071818560110592
   2. mailto:rsdio at audiobanshee.com
   3. mailto:coreyker at gmail.com
   4. mailto:Synth-diy at synth-diy.org
   5. http://synth-diy.org/mailman/listinfo/synth-diy