[sdiy] Oberheim Xpander Multimode VCF Question

[David G. Dixon]

Hey Team!

I just sent Steven my Excel file "Pascal Filter" which has equations for
every transfer function you can think of with a four-stage multimode filter,
and a working model which allows you to see the output for any combination
of stage gain factors and resonance feedback gain (as a percentage of
self-oscillation gain, up to 99%).  If you would like to receive your own
copy, please email me offline.


> Thanks for this, Magnus. I see what you mean about my use of '-24dB/oct' -
> perhaps I should have said 4 pole. I think I've made another mistake as
> well: (+) and (-) are swapped in my example, so it should have been:
> 
> input - pole1*3 + pole2*6 - pole3*4
> 
> I still don't really understand the math(s), though. Is it possible to
> work
> out by educated guesswork, like by noting that the allpass given above
> consists of a 24dB highpass minus a 24dB lowpass and a 6dB lowpass? I'm
> thinking, get rid of the 6dB lowpass contribution and end up with:
> 
> input - pole1*4 + pole2*6 - pole3*4
> 
> Or am I barking up the wrong tree?
> 
> Steven Cook.
> 
> http://www.spcplugins.com/
> +44(0)1271 867288
> 
> 
> --------------------------------------------------
> From: "Magnus Danielson" <magnus at rubidium.dyndns.org>
> Sent: Thursday, March 11, 2010 11:04 AM
> To: "Steven Cook" <stevenpaulcook at tiscali.co.uk>
> Cc: <synth-diy at dropmix.xs4all.nl>
> Subject: Re: [sdiy] Oberheim Xpander Multimode VCF Question
> 
> > Steven Cook wrote:
> >> Hi,
> >>
> >> Is it possible to get a -24dB/oct allpass response out of an Oberheim
> >> Xpander type of 4-pole filter arrangement? I've got the following for
> >> an -18dB allpass, from a post by David G. Dixon...
> >>
> >> input + pole1*3 - pole2*6 + pole3*4
> >>
> >> Which seems to work fine (in software).
> >
> > I'm in a hurry, so you will not get the complete answer now... from me
> at
> > least.
> >
> > First of all, you can't talk about -24 dB/Oct slope for an all-pass
> > filter. While I am happy that you say -24 dB/Oct for low-pass, it is
> > meaningless for all-pass as they are 0 dB/Oct. This only once again
> brings
> > out the point... the slope does not tell how many poles and zeros there
> is
> > in a filter, just how many there at least needs to be.
> >
> > Now, the actual question is, can you create a 4-pole/4-zero all-pass
> > filter from the Xpander module? The quick answer is yes.
> >
> > What I don't have time to help you with is how to combine the outputs
> from
> > the different taps, but you are on the right path when you combine input
> > with the taps.
> >
> > For non-complex poles, you have (s+a)/(s-a) for each stage. For complex
> > poles (s+a-jb)(s+a+jb)/(s-a-jb)/(s-a+jb). Notice how the real term a
> shift
> > sign from poles to zero. Any all-pass filter is then just a combination
> of
> > those using various sets of a and b. You should be able to pull it out
> > from there with some paper-and-pen work, which is the thing I don't have
> > time for right now.
> >
> > If you still have problem, let me know. I might be able to do the
> homework
> > for you later.
> >
> > Cheers,
> > Magnus
> 
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