On 11 November 2013 18:26, Marco Lo Monaco wrote:
> Hi Ross/Andrew,
> I couldnt wait to put my hands on it :) (the creativity/curiosity spark is
> always lit)
>
> Here is my MuPad notebook :
>
> https://www.dropbox.com/s/er1s0aeheuv3igg/VCF-StateVariableFilter.pdf
>
> I basically demonstrate what I already said in my previous posts.
> The standard state-space approach leads to identical results to your
> algorithm, I would say even without the trick of the TPT, because of course
> we are talking about an instantaneous _linear_ feedback.
> That makes sense: "my" ABCD statespace matrixes are identical to "yours",
> same thing applies for CPU load in terms of MULs/ADDs.
>
>
Hi Marco,
Thanks very much as well must go to you for doing this analysis. I'm not
familiar enough with this decomposition to be of much use providing
feedback at the moment sorry!
The two sets of matrices are indeed the same, but I am worried that this
may only be the case in the LTI case since the function you used to
generate the first set is StateSpaceBilinear which sounds like there is a
layer of abstraction going on but I don't know for sure what that function
is doing.
Can you please confirm that the final actual number crunching is the same
in the final implemenation?
ie the same + - * and / on the same variables that leads to the same actual
numerical performance if both are done out in full.
Of course the main purpose of my analysis was to keep in mind that you will
> _always_ have to deal with an "implicit"/hidden inversion of a matrix A of
> the analog system (actually (I-A*h/2)) of the same order of your system,
> which in this SVF fortunate case is 2 and also easy. For a moment think
> about an analog system who has 10 capacitors and you want it to change it
> at
> audio rate: you will have to deal with a0,a1,a2... coeffs that will be
> rationaly polynomials, meaning lots of DIVs at runtime). Generally
> speaking,
> inverting a matrix at audio rate is not a good idea :)
>
Don't get hung up on the matrix thing, it's not that important. You can
solve these things with basic linear algebra too, they are all equivalent.
It is just solving n linear equations for n unknowns that is important.
> As I already said, we agree that these approaches are dated a long ago.
>
> Ross showed the same results of matrix A,B (he didn't showed C,D because
> they are not needed for the Laroche BIBO analysis). His results match my
> same ones.
>
> Sorry if I omitted some code in collecting state/in/out variables in your
> original algo, but I already got 6 pages of pdf this way and I thought it
> would have been a good idea to keep it simple.
>
> Hope to have helped you clear my my point of view.
>
> Ciao
>
> Marco
>
Thanks Marco I appreciate your help!
All the best,
Andy
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