just resurrecting this old post. I'm curious has anyone implemented a ”topology
preserving” filter in faust?
this SVF is really nice
https://cytomic.com/files/dsp/SvfLinearTrapOptimised2.pdf
<https://cytomic.com/files/dsp/SvfLinearTrapOptimised2.pdf>
> On 24 Apr 2014, at 08:56, D <d...@mailismagic.com> wrote:
>
> Julius Smith <jos@...> writes:
>
>>
>>
>> I guess there are multiple definitions of "computable". In the
>> papers I've read (e.g., on wave digital filters), a delay-free loop
>> is said not to be computable. Solving the linear set equations for a
>> solution
>> gives you a new flow graph - a new filter structure that's computable as
>> drawn.
>>
>
> Hi Julius,
>
> Thanks for your reply. I've never quite understood the mathematical
> significance of the different approaches so I really appreciate your
> thoughts on the topic.
>
> I know of the topology rearrangement for avoiding delay-free loops,
> for example in "Detection, Location, and Removal of Delay-Free
> Loops in Digital Filter Configurations".
>
> However, from what I understand of both Vadim's an Raph's approach
> is that they are "topology preserving". Specifically the state variables
> from the equations I posted in my previous mail matches the voltages
> on the capacitors (trapezoidal integration of current) of a similar analog
> circuit, 4 1-pole filter in series with a feedback path of gain -k.
>
> Additionally Raph's State Space Representation is also the identical
> "topology", so I don't understand how this approach results in a
> "new flow graph".
>
> Raph's notebook specifically cites your paper. As an additional
> citation besides Raph and Vadim, there is some discussion of the
> "topology preserving transform" from WIll Pirkle:
>
> http://www.willpirkle.com/Downloads/AN-4VirtualAnalogFilters.2.0.pdf
>
> Since I am usually not working on the block-diagram level, but so
> far have understood things more just as a "set of equations", and
> perhaps since the integration is implicit, that's what allows you to
> solve the delay-free loop? I've never exactly understood the
> mathematical implications here.
>
> Thanks very much!
>
>>
>> A related term in the finite-differences world is "implicit" versus
>> "explicit"
>> finite difference schemes, where implicit means you have to solve some
>> simultaneous equations and explicit means you can compute forward
>> each time step using previously computed values (a "causal" recursion).
>>
>> So, maybe it's just terminology...
>>
>> - Julius
>>
>>
>
>
>
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