[music-dsp] Name of delay-free loop technique
vadim.zavalishin at native-instruments.de
Tue May 26 06:31:20 EDT 2009
> 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
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.
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