[sdiy] Digital 4 Pole Multimode Filter

[Andrew Simper]

Hi Scott,

I asked why do you want a four pole SVF since mostly two 2 pole SVFs
cascaded is more versatile. It sounds like there is no compelling reason,
so you just stick with two 2 pole SVF. I've written multiple technical
papers on the subject which you can grab here:

https://cytomic.com/tecnical_papers

At the top are SVF ones to do with direct trapezoidal integration with
various tradeoffs in ease of implementation vs numerical performance, and
at the bottom is a version that adds coefficient warping and explicit
averaging to match the frequency response and stability of a Forward Euler
(FE) SVF to that of the trapezoidal one (TR). This includes 3 different
variations on FE, including the well known Hal Chamberlin form. All forms
are stable across the entire frequency and resonance range up to Nyquist,
but do require a division (or approximation thereof) with change in cutoff
and damping.

The same warping can be applied to the Sallen Key FE filter, and any other
two pole realisations for that matter. I tried it with four poles but the
quartic rational polynomials were unyielding to my basic approaches and
most likely the solution would be more complicated than just direct solving
of the trapezoidal integration anyway so I left it well alone!

Now having said all that, the four pole SVF does sound different in the
non-linear case compared with two cascaded 2 pole SVFs, and you also have
less mathematical summing gymanstics generating a simultaneous four pole
high pass and low pass outputs if your damping isn't that of an LR4, so
there are still some edge cases where a single 4 pole SVF is better.

Cheers,

Andy


On 4 May 2018 at 00:20, Scott Gravenhorst <music.maker at gte.net> wrote:

>
> Thank you to all who replied.
>
> Very helpful information.
>
> Someone asked why I wanted a 4 pole SVF.  In fact, I merely wanted a
> multimode 4 pole
> filter, and I'd read that SVF can have 2 or more poles.  So a sort of "why
> not?" thing.
>
> The comments about cascading 2 pole SVFs made a lot of sense.  The modes
> are easily
> available.  I'm assuming that if I want 4 poles of highpass, I would take
> the HP out of
> the first SVF and put that on the input of the second SVF also set to
> highpass and make
> the Fc the same for both to get the -24 dB/oct falloff.  Same with BP et
> al.  And the
> idea of cascaded two SVFs with unlike Fc is also appealing.  It seems a
> very versatile
> system which is exactly what I want.
>
> Now tackling Q enhancement, but that's pretty trivial.
>
> -- ScottG
> ________________________________________________________________________
> -- Scott Gravenhorst
> -- http://scott.joviansynth.com/
> -- When the going gets tough, the tough use the command line.
> -- Matt 21:22
>
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