[sdiy] Low Cost Comb Filter Methods

[rsdio at audiobanshee.com]

On Jun 14, 2018, at 6:32 AM, Andrew Simper wrote:
> On Tue, 12 Jun 2018 at 16:00, Brian wrote:
>> Meanwhile, the help I was looking for was commentary on whether a 3-capacitor op-amp circuit would actually be straightforward to simulate / emulate in software. One of these days I’m going to have to learn how to use the Z-transform to convert a circuit diagram into lines of code. Seems like it should require only three words of state memory and a few cycles of math.
>> 
>> Brian
> 
> That would be my cue :)
> 
> Yes, very easy to model in the linear case, but you will most likely be better off just using a linear SVF if you want a whole bunch of them as it will be way more efficient. The point of the design I think is you could use a single op-amp per resonator, an SVF uses 3, but in digital it's cheaper to just use an SVF since perfect opamps are free. The only point I can see in preserving the structure of the filter in the paper would be if you used Boyle macro model for the op-amp so you would get some non-linear saturation effects in the implementation, but then things get quite a bit more complicated.
> 
> If anyone is interested in the linear case then here are the equations to solve the circuit:
> https://cytomic.com/files/dsp/comb-filter-resonator-equations.pdf
> 
> and here is an implementation in python generator by my circuit solver:
> https://cytomic.com/files/dsp/comb-filter-resonator.py
> 
> and a plot of the filtering of a sawtooth given one set of component values:
> https://cytomic.com/files/dsp/comb-filter-resonator.png
> 
> Cheers,
> 
> Andy

Excellent. Thanks!

There’s one error in your reproduction of the schematic, though. rp is not supposed to be grounded, but should be connected to the +V supply. How much does that change the equations? It should reverse the current through the resistor, at the very least.

Brian