On 08-Nov-13 03:13, Ross Bencina wrote:
Now, I do have one thing I would like to see: and that is a mathematical
proof that point (4) above is actually true for this topology. Ever
since I read the Laroche BIBO paper it scared the crap out of me to be
modulating any IIR filter at audio rate without a trusted analysis.
Hi Ross,
I once tried to do the analysis you mentioned. IIRC, I managed to
successfully show the time-varying BIBO stability of analog 1-pole (this
is very simple) and 2-pole (somewhat more tricky) analog SVFs under the
condition that the real parts of all poles are "uniformly negative"
(that is bound by some negative constant from above). IIRC, it is also
quite straightforward to show the time-varying stability of a 2nd-order
real Jordan cell (which probably has the best time-varying stability
anyway), but this one is not so convenient as the LP/BP/HP multimode
SVF. I have no idea if there are papers addressing this.
For the discrete-time versions it seemed way more complicated. I
couldn't prove it or build a disproving example for the TPT BLT version
of the same 2-pole SVF (and I don't remember whether I managed to build
a proof for the 1-pole).
Regards,
Vadim
--
Vadim Zavalishin
Reaktor Application Architect
Native Instruments GmbH
+49-30-611035-0
www.native-instruments.com
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