About this zero-delay feedback again (sorry)

[Z1202]

This approximation still needs to preserve the amplitude-phase relationship, therefore such rational transform function necessarily needs to have identical orders of numerator and denominator.

I don't see why it would be necessarily to this exactly, except at resonant frequencies. Errors in such approximation will obviously distort the response, but if the end result is closer to the ideal than what you get after the frequency warping, does it matter?

As I wrote earlier, for me preserving the amplitude-phase relationship is having high priority. Because I intuitively expect this to be audible in certain cases, even if only subconsciously. I don't have an experimental proof however . Also you can use these filters further without much thinking. If that's not a must for you, of course you can relax this constraint.

[cheppner]

This approximation still needs to preserve the amplitude-phase relationship, therefore such rational transform function necessarily needs to have identical orders of numerator and denominator.

I don't see why it would be necessarily to this exactly, except at resonant frequencies. Errors in such approximation will obviously distort the response, but if the end result is closer to the ideal than what you get after the frequency warping, does it matter?

How about

Code: Select all

1/4 * (1 + 4z^-1 - z^-2)/(1-z^-1)

as an integrator?

Hmm, looks interesting in the time domain but near nyquist it doesn't give us much. Hmm. But how about the general idea of using higher order integrators?

[Z1202]

How about

Code: Select all

1/4 * (1 + 4z^-1 - z^-2)/(1-z^-1)

as an integrator?

Hmm, looks interesting in the time domain but near nyquist it doesn't give us much. Hmm. But how about the general idea of using higher order integrators?

I wonder if higher order integrators could have group delay-related issues ("too high latency"). Also the stability of the transform needs to be checked.

[cheppner]

Maybe this or this sheds some light...

[mystran]

Maybe this [...] sheds some light...

No, not really. I think that's the wrong approach, really. If I understand correctly they try to replace the bilinear integrator with a higher-order replacement (and then compare a bunch of variations), but that's not really what I had in mind.

I was rather thinking about choosing (or "designing") the integrator once we already have the target response, in order to optimize the transformed response. Note that in this case it's not really even necessary for a given integrator to be stable except for a particular set of poles (those that are actually present in the target filter) because once the poles move, we can redesign the integrator such that the new one is stable for the new set of poles.

This isn't exactly a new idea. I was just wondering whether anyone has any experiences from integrating that kind of stuff into the TPT context. Apparently, if someone has done it, they don't want to admit anything, so nevermind.

[christripledot]

*snip*

Never mind. Read more, finished being stupid, got something working.