okay, so that's an analog resonant LPF filter. there is a method, called "impulse invariant" (an alternative to BLT) to transform this analog filter to a digital filter. as it's name suggests, we have a digital impulse response that looks the same (again, leaving out the unit step gating function):
Just for the record. The digital impulse response indeed looks exactly the same, but (!) it is not bandlimited, which results in distorted frequency response of the resulting filter. Bandlimiting the response is not a solution either, because the resulting response then is not a response of a system consisting of a finite number of unit delays.
Vadim, is this the article you meant? Fontana, "Preserving the structure of the Moog VCF in the digital domain" Proc. Int. Computer Music Conf., Copenhagen, Denmark, 27-31 Aug. 2007 http://quod.lib.umich.edu/cgi/p/pod/dod-idx?c=icmc;idno=bbp2372.2007.062
Yes, thanks Martin. BTW, I'f I'm correct, this paper (I only briefly looked through it) doesn't address fixing the problem in the 1-pole components. It's correct that the bigger problem is in the outer feedback loop, but performing the same fix in the 1-poles improves the behavior further, IIRC.
-- it does beg the question: why didn't we think of this earlier? and why did Chamberlin do it the way he did?
A number of people *did* think of this earlier, also in the application to the analog simulation. E.g. the simulanalog.org article I mentioned earlier uses trapezoidal integration, and I would guess that there is even some earlier work. The right question is: why almost nobody cares about this issue?
Yet another issue, is the subjectivity of the judgement. Not all DSP engineers, and even not all musicians have the same high requirements to the details of the filter response. Many people would be fully happy with the Chamberlin SVF as it is. Also, BLT filters require division (once the parameters change), which was quite expensive, especially those days, I think.
Regards, Vadim -- Vadim Zavalishin Senior Software Developer | R&D Tel +49-30-611035-0 Fax +49-30-611035-2600 NATIVE INSTRUMENTS GmbH Schlesische Str. 28 10997 Berlin, Germany http://www.native-instruments.com Registergericht: Amtsgericht Charlottenburg Registernummer: HRB 72458 UST.-ID.-Nr. DE 20 374 7747 Geschaeftsfuehrung: Daniel Haver (CEO), Mate Galic -- 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
