[sdiy] 3 Pole state-variable filters

[Magnus Danielson]

From: "jhaible" <jhaible at debitel.net>
Subject: Re: [sdiy] 3 Pole state-variable filters
Date: Tue, 12 Feb 2002 02:40:47 +0100

Jürgen,

> > In the style of Matrix-12/Xpander: BP2+AP, LBP and HBP
> >
> > That is, you can either balance a zero with a pole and avoid slopes,
> > or you use it on either side of the passband to create a 12dB/Oct-6
> > dB/Oct division between sides. In the allpass case you have 6dB/Oct
> > slopes on both sides.
> 
> So you either spend one real pole (not compensated by a zero) for
> an extra LPF or HPF (assymmetrical slopes), or you're compensating
> the real pole with a zero to make an all pass, resulting in a
> non-minimal-phase BPF filter. Ok, no need to choose the zero
> equal to the negative real pole, so there would be other ways to preserve
> symmetrical slopes than adding a pure all pass. Remaining question is
> can I get anything different in amplitude response than from a 2pole
> BPF, or is there just an extra degree of freedom for phase ?

If you want to stick to equal slopes, then yes, different phase is
what you get. You can also level out the slope on one side, to get

           |
       ____|_
      /     \
     /       \
----/         \
               \
                \

If that would be usefull. 

The slopes are from the BP part, you level the bottom slope out with
the extra pole and you can let the third zero add to the upper slope
or put it way up. Notice that you in addition have a resonance from
the complex pole pair to play with. Above I just played fun with it.

Is it usefull? You tell me! I'm just saying you can do this kind of
stuff. I'm just toying with theory here, just mildly
motivated. Motivate me more and I take no responsibility! ;O)

Cheers,
Magnus