This very much wipes out the possibility of a general purpose analog structure that can sort of "stabilize" (if I may say) an arbitrary Z domain transfer function.Z1202 wrote: ↑Fri Apr 26, 2019 4:23 am@S0lo. I'll try to take a look at your paper later. Two notes:
1) I'm not sure the structure diagram you posted is cutoff-modulation-stable, because the modulation stability is guaranteed for having cutoff controls in front of the integrators only (see 2.7 of the book), whereas in your structure the cutoff control seems to be spread across the structure. Typically the cutoff control is assumed to be embedded into the integrators, and a and b coefficients controlling other aspects of the filter, e.g. resonance. Also see 2.16 explicitly requiring in the beginning: "Suppose the cutoff gain elements are always preceding the integrators and suppose all integrators have the same cutoff gain (that is, these gains always have the same value, even when modulated)."
In a previous post, I tried to do inverse BLT to match the TPT-SVF (almost the same one in the book). It didn't work. http://www.solostuff.net/wp-content/upl ... e-BLTt.pdf
Edit: Basically there was no solution. More equations than unknowns.
I will make sure I check. looks interesting indeed.Z1202 wrote: ↑Fri Apr 26, 2019 4:23 am2) There is a TPT way to control the cutoff of digital structures directly, which is based on the discrete-time cutoff substitution formula. It also preserves the original topology of the digital system. Essentially you can replace each z^-1 with a 1-pole allpass. By controlling the cutoffs of the allpasses you can control the cutoff of the entire filter. Taking TPT 1-pole allpasses you ensure stability in modulation. It's roughly described here
https://www.native-instruments.com/file ... caling.pdf
although the argument in the paper could have been done in a better way.
Sure, but again how can we insure stability using an arbitrary S domain transfer function while we know it's not going to be LTI.Z1202 wrote: ↑Fri Apr 26, 2019 4:23 amOne more edit: literally skimmed though your article. A note: you can do pole-zero design in ZDF/TPT using analog plane exactly the same way how you do pole-zero in z-plane. And I think the reasoning is usually easier in the s- than in z-plane, since the frequency axis is fully linear.