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

Martin Eisenberg martin.eisenberg at udo.edu
Mon Jun 8 18:01:38 EDT 2009

Vadim Zavalishin wrote:

> Except that you have introduced a different time scale, where
> t_end=infinity occurs before y[n] (or at the same time).

I thought of this as happening outside true time. A matter of
taste, I guess.

>> Do you know any analog devices, besides perhaps
>> oscillators, that routinely operate that way? Have you
>> generally found it sufficient to solve the system as if linear
>> and then saturate the result?
> Of course generally it's not sufficient.

I have a feeling you've answered a different question than I
intended -- have you mostly been satisfied with the cheap

> Instantaneously unstable cases
> will correspond to the horizontally-reverted graph of
> g*tanh(x-ky), where the graph's steepness (derivative) must
> exceed 1, in which case the system "wants" to go into the
> opposite direction of the intersection of the h(y)=y-s and the
> nonlinearity's tangent line (I think).

I can't quite picture it. Tangent line where -- at the steepest
point? And by "in the opposite direction of", do you mean "away
from" the intersection? I'd guess you do because that
interpretation does make the selection unique; namely, the
solution jumps from one outside branch of the multivalued inverse
function to the other as soon as the input enters the latter's
support. Is that what you're saying?


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