[sdiy] Multi-output comb filter?

[rsdio at audiobanshee.com]

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.

Here’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 you’d end up with a single delay tap? I mean, that’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 they’re equivalent to a single, long delay so long as nothing taps the intermediate samples.

I have a suspicion that things wouldn’t quite work out so perfectly, and there’s be lots of taps, each with their own weight, and it wouldn’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