[sdiy] 3 Pole state-variable filters

[UrosM]

hi people

> > LPF or HPF).  Or is there a way to "distribute" 3 poles equally
> > on both slopes of a BPF function ?

>       s^2 + s
> -----------------
> s^3 + s^2 + s + 1
To be picky this is not BPF , this is oscillator ;)
(sorry had to do it )


> > 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 ?
> 
> JH.
Nope . You get bp2+ap only if zero is positive . Else if zero is 
negative and Wz not equal Wp you get various responses that dont fall
into categories Magnus mentioned above , but none of them would be
"symmetrical" .

interesting side note : I guess most of people know this but for those
who dont ( I myself discovered it two weeks ago ) : Summing LP and BP
outs of state variable filter will give you "-6dB LP" with resonance
( (s+1)/(s^2+s+1) in case of normalized butterworth )
of course hp +bp will give +6dB HP .

ypow