[music-dsp] zero delay feedback for phase modulation synthesis?

[gm]

I wonder if anyone has thought about this?

I am aware that it may have little practical use and may actually worsen the
"fractal noise" behaviour at higher feedback levels.
(Long ago I tested this with a tuned delay in the feedback path and
thats what I recall)
But still I am interested.

If the recurrence for the oscillator with feedback is:

y[n] = ( 1/(2Pi) * sine(2*Pi* y[n-1]) + k) mod 1

there are two nonlinearities and it's all above my head...

[Vadim Zavalishin]

I think people have thought about this (IIRC at least I heard from one
of the U-He guys that he tried zero-delay feedback FM). I'm not sure
what's the origin of your equation, but then I'm not into phase
modulation synthesis. Anyway, I suspect in certain excessive nonlinear
situations there is no solution whatsoever. E.g. consider the
zero-feedback equation of the form

x = a*x + b*y
y = b*x - a*y
where x,y are signals and a and b are coefficients such that a^2+b^2=1
(actually this equation is linear, but I think you get the idea).

Some basic thoughts on the rising issues (and on how to solve your
equation) can be found in Section 3.13 of this text:

https://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/VAFilterDesign_2.1.0.pdf

Plus the usual numerical nonlinear solution techniques of course (where
Sections 6.4-6.8 and 6.10 may be of interest).

Regards,
Vadim

Post by gm
I wonder if anyone has thought about this?
I am aware that it may have little practical use and may actually worsen the
"fractal noise" behaviour at higher feedback levels.
(Long ago I tested this with a tuned delay in the feedback path and
thats what I recall)
But still I am interested.
y[n] = ( 1/(2Pi) * sine(2*Pi* y[n-1]) + k) mod 1
there are two nonlinearities and it's all above my head...
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