Thanks for the links, Steven!

Vadim, what is the title of your book? We may have it here at uni.

Hi, Robert. I'm working on some time-domain feature-extraction algorithms
based on adaptive mechanisms. A couple of years ago, I implemented a
spectral tendency estimator where the cutoff of a crossover (1p1z filters)
is piloted by the RMS imbalance of the two spectra coming out of the same
crossover. Essentially, a negative feedback loop for the imbalance pushes
the cutoff towards the predominant spectrum until there's a "dynamical
equilibrium" point which is the estimated tendency.

A recent extension to that algorithm was to add a lowpass filter within the
loop, at the top of the chain, as shown in this diagram:
https://www.dropbox.com/s/a1dtk0ri64acssc/lowest%20partial.jpg?dl=0. (Some
parts necessary to avoid the algorithm from entering attractors have been
omitted.)

If the same spectral imbalance also pilots the cutoff of the lowpass
filter, we have a nested positive (the lowpass strengthens the imbalance
which pushes the cutoff towards the same direction) and negative (the
crossover's dynamical equilibrium point) feedback loop. So it is a
recursive function which removes partials from top to bottom until there is
nothing left to remove except the lowest partial in the spectrum.

The order and type of the lowpass (I've tried 1p1z ones, cascading up to
four of them), I believe, is what determines the SNR in the system, so what
the minimum amplitude of the bottom partial should be to be considered
signal or not. Large transition bands in the lowpass will affect the result
as the top partials which are not fully attenuated will affect the
equilibrium point. Since elliptic filters have narrow transition bands at
low orders, I thought that they could have given more accurate results,
although the ripples in the passing band would also affect the SNR of the
system.

Perhaps using Butterworth filters could be best as the flat passing band
could make it easier to model a "threshold/sensitivity" parameter. With
that regard, I should also have a look at fractional order filters. (I've
quickly tried by linearly interpolating between filters of different orders
but I doubt that that's the precise way to go.)

Of course, an FFT algorithm would perhaps be easier to model, though this
time-domain one should be CPU-less-expensive, not limited to the bin
resolution, and would provide a continuous estimation not limited to the
FFT period.

I've tested the algorithm and it seems to have a convincing behaviour for
most test signals, though it is not too accurate in some specific cases.

Any comment on how to possibly improve that is welcome.

Thanks,
Dario


Dario Sanfilippo - Research, Teaching and Performance
Reid School of Music, Edinburgh University
+447492094358
http://twitter.com/dariosanfilippo
http://dariosanfilippo.tumblr.com

On 3 February 2018 at 08:01, robert bristow-johnson <
r...@audioimagination.com> wrote:

> i'm sorta curious as to what a musical application is for elliptical
> filters that cannot be better done with butterworth or, perhaps, type 2
> tchebyshev filters?  the latter two are a bit easier to derive closed-form
> solutions for the coefficients.
>
> whatever.  (but i am curious.)
>
> --
>
> r b-j                  r...@audioimagination.com
>
> "Imagination is more important than knowledge."
>
>
>
> ---------------------------- Original Message ----------------------------
> Subject: Re: [music-dsp] Elliptic filters coefficients
> From: "Dario Sanfilippo" <sanfilippo.da...@gmail.com>
> Date: Fri, February 2, 2018 6:37 am
> To: music-dsp@music.columbia.edu
> --------------------------------------------------------------------------
>
>
> > Thanks, Vadim.
> >
> > I don't have a math background so it might take me longer than I wished
> to
> > obtain the coefficients that way, but it's probably time to learn it.
> With
> > that regard, would you have a particularly good online resource that
> you'd
> > suggest for pole-zero analysis and filter design?
> >
> > Thanks to you too, Shannon.
> >
> > Best,
> > Dario
> >
> > On 1 February 2018 at 11:16, Vadim Zavalishin <
> > vadim.zavalis...@native-instruments.de> wrote:
> >
> >> Hmm, the Wikipedia article on elliptic filters has a formula to
> calculate
> >> the poles and further references the Wikipedia article on elliptic
> rational
> >> functions which effectively contains the formula for the zeros.
> Obtaining
> >> the coefficients from poles and zeros should be straightforward.
> >>
> >> Regards,
> >> Vadim
> >>
> >>
> >> On 01-Feb-18 12:00, Dario Sanfilippo wrote:
> >>
> >>> Hello, everybody.
> >>>
> >>> I was wondering if you could please help me with elliptic filters. I
> had
> >>> a look online and I couldn't find the equations to calculate the
> >>> coefficients.
> >>>
> >>> Has any of you worked on that?
> >>>
> >>> Thanks,
> >>> Dario
> >>>
> >>>
> >>> _______________________________________________
> >>> dupswapdrop: music-dsp mailing list
> >>> music-dsp@music.columbia.edu
> >>> https://lists.columbia.edu/mailman/listinfo/music-dsp
> >>>
> >>>
> >> --
> >> Vadim Zavalishin
> >> Reaktor Application Architect
> >> Native Instruments GmbH
> >> +49-30-611035-0
> >>
> >> www.native-instruments.com
> >> _______________________________________________
> >> dupswapdrop: music-dsp mailing list
> >> music-dsp@music.columbia.edu
> >> https://lists.columbia.edu/mailman/listinfo/music-dsp
> >>
> >>
> > _______________________________________________
> > dupswapdrop: music-dsp mailing list
> > music-dsp@music.columbia.edu
> > https://lists.columbia.edu/mailman/listinfo/music-dsp
>
>
>
> _______________________________________________
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