Chamberlain state variable filter - unity gain
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- KVRian
- 513 posts since 3 Sep, 2009 from Poland
I am looking for a variable bandwidth bp filter with easy sample rate modulation. I assume state variable is the best option here, but how can I normalise its output? (resonance peak value = 1)
giq
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- KVRAF
- 8491 posts since 12 Feb, 2006 from Helsinki, Finland
I'd forget Chamberlin unless you are specifically interested in emulating legacy digital synths, as the "ZDF" models for SVF don't use singnificantly more CPU and behave much more predictably and closer to how you would expect, with proper separation of cutoff and Q.
See for example: http://www.kvraudio.com/forum/viewtopic ... 1#p4913251
In an analog SVF (and hence the ZDF models) the band-pass gain at cutoff is exactly Q, so in some sense the filters are normalized already. If you would instead prefer to have 0dB peak-gain, simply divide the output by the Q value. Note that since you only ever need 1/Q there is no problem getting all the way to self-oscillation as Q reaches infinity (the limit for the division is then simply 0).
See for example: http://www.kvraudio.com/forum/viewtopic ... 1#p4913251
In an analog SVF (and hence the ZDF models) the band-pass gain at cutoff is exactly Q, so in some sense the filters are normalized already. If you would instead prefer to have 0dB peak-gain, simply divide the output by the Q value. Note that since you only ever need 1/Q there is no problem getting all the way to self-oscillation as Q reaches infinity (the limit for the division is then simply 0).
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- KVRAF
- 8491 posts since 12 Feb, 2006 from Helsinki, Finland
The analog bandpass has a (frequency normalized) transfer function s/(s^2+s/Q+1), so if we set s=i*w with w = 1 (cutoff), we get i/(i^2 + i/Q + 1) and since i^2 = -1, this simplifies to i/(i/Q) = Q, which is then the response at cutoff. That linear relationship stays exact with bilinear transform (which only warps frequencies), which is what the ZDF stuff is based on.itoa wrote:Thanks a lot! I've seen this on spectrum, but thought this relation is nonlinear
This one is needed for variable width pitched noise.
It won't work properly with Chamberlin though; in that case the would be some interdependence between cutoff and Q and the relation between Q and gain would depend on the cutoff. You can still solve the gain from the digital transfer function if you really want to, but I won't do it, because I don't think it's worth the trouble.