[music-dsp] Name of delay-free loop technique

[Vadim Zavalishin]

> This is what I referred to in my article as "non-zero impedance approach". 
> I believe you could explicitly obtain the same result with the approach of 
> the Harma's article you pointed me to, except instead of a unit delay 
> running at a very high sampling rate in the feedback path you need to use 
> a lowpass filter with a very high cutoff running at a very high sampling 
> rate. I once did the same in the continuous time domain, obtaining similar 
> results.

Correction: you should rather do it in the continuous time domain. So the 
main part of the discrete-time structure is frozen in time, while the 
delayless feedback is considered to be continuous-time. Now insert a lowpass 
filter into the feedback. Let f be the filter cutoff. Let the feedback run 
over the time period deltaT. Now let f approach infinity and deltaT approach 
zero, where f is approaching infinity "faster" than deltaT is approaching 
zero, so that their product is approaching infinity. If such system is 
unstable, then I'd say that the delayless feedback is "instantly unstable" 
and the value reaches infinity "within a single sample". Otherwise the 
delayless feedback converges to the point of stability within the same 
sample and you can simply solve the feedback equation.

Notably, while for the ladder filter the instantly unstable case occurs in a 
rather exotic negative resonance case k<-1, for a state-variable filter you 
get it for very strong resonances (1/Q<-2). This information is sometimes 
important when nonlinearities are introduced.

Regards,
Vadim

-- 
Vadim Zavalishin
Senior Software Developer | R&D

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