(the quotation is from Andy's mail)
On 2/8/13 2:15 AM, Ross Bencina wrote: i've analyzed Hal's SVF to death, and i was exposted to Andy's design some time ago, but at first glance, it looks like the "Trapazoidal SVF" looks like it doubles the order of the filter. it it was a second-order analog, it becomes a 4th-order digital. but his final equations do not show that. do those "trapazoidal" integrators, become a single-delay element block (if one were to simplify)? even though they ostensibly have two delays?
You can use canonical (DF2/TDF2) trapezoidal integration, in which case the order of the filter doesn't formally grow. This is quite intuitively representable in the TPT papers and the book I mentioned earlier. If you use DF1 integrators, the order formally grows by a factor of 2, but I believe half of the poles will be cancelled by the zeroes.
BTW, IIRC, as for the optimization from 4 z^-1 to 3 z^-1 in Andy's SVF, I believe this optimization implicitly assumed the time-invariance of the filter. So, while keeping the transfer function intact, this optimization changes the time-varying behavior of the filter (not sure, how much and whether it's for the worse or for the better).
Regards, Vadim -- Vadim Zavalishin Reaktor Application Architect Native Instruments GmbH +49-30-611035-0 www.native-instruments.com -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
