# [music-dsp] SVF stability limit final graphs

eli+ at gs211.sp.cs.cmu.edu eli+ at gs211.sp.cs.cmu.edu
Fri Nov 2 15:12:21 EST 2001

```andy at vellocet.com wrote:
> http://www.vellocet.com/dsp/svf/svf-stability.html
>
> The page shows that 2/F - F/2 or equivalently -Q + sqrt(4 + Q^2) is the
> correct limit for an implementation of the state variable filter to follow
> the theory.

So I believe you're comparing digital SVF output versus digital SVF
theoretical values.  Wouldn't it make more sense, musically, to
compare versus the analog SVF?

What you're measuring is roundoff error plus instability --
practically, a stability plot of the digital SVF.  But the digital SVF
(Chamberlin's discretization) is different from the analog one.  The
squawky highpass behavior that I think we're trying to avoid is built
in to the digital SVF.

For example, consider F = 1.8, Q = 0.1, which is inside the stability
bound.  For these arguments, as your plot shows, the digital SVF
implements its own theory pretty much exactly.  But look at it:
http://www.cs.cmu.edu/~eli/tmp/svf/svf_f1.8_q0.1.png
That's the _lowpass_ output.

Your approach of measuring actual minus ideal amplitude response at
Nyquist seems a good way to go (nicer than my "nonlowpassness" hack).
I'd just define "actual" as digital (from experiment or the transfer
function, doesn't much matter), and "ideal" as analog (from the
s-domain transfer function).

--
Eli Brandt  |  eli+ at cs.cmu.edu  |  http://www.cs.cmu.edu/~eli/

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