[sdiy] Digital 4 Pole Multimode Filter

[Andrew Simper]

Wrong link in the previous email sorry! Should have been:

https://cytomic.com/technical-papers

Cheers,

Andy

On 4 May 2018 at 03:32, Andrew Simper <andy at cytomic.com> wrote:

> 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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>
>
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