If there are zeroes on the unit circle in the z-plane, I don't think it will be a very good all-pass filter... (Because some sinusoid frequencies would be blocked entirely)
Neat topic so far! I'd love to see an illustration of this real-line "zebra stripe" design. Also wondering what sort of filter a similar pattern on the imaginary line produces! (I should improve my own filter testbed...) – Evan Balster creator of imitone <http://imitone.com> On Mon, Feb 6, 2017 at 8:57 PM, Sampo Syreeni <de...@iki.fi> wrote: > On 2017-02-06, Eric Brombaugh wrote: > > well, with a single sinusoid, there should be no intermodulation product >>> so the analytic envelope should be exactly correct. but consider: >>> >> [...] > > I might be way off base here, but... As Olli said, both the poles and the > zeroes sorta "like to be" on the real line. > > To me that is kind of a canary. Typically when something works on the real > line, it tends to work better when distributed over the unit circle. Often > even reflected over the unit point. > > Olli, I *know* this is again highly intuitionistic. But could you still, > as the kind of guy who actually follows through with his math, check this > out? I am reasonably, intuitionistically sure, that you started your > optimization from a local basin. I'm pretty sure there is at least one > other basin even given your optimization criteria, given by alternating > zeroes and poles over the left half of the unit circle over the z-plane, > just as you said they worked alternately over the real line. Or perchance > over some elliptical locus. > > Please, try that original setup as well. Then tell us what your > optimization machinery did with it. I'm reasonably sure it wouldn't > converge to what you originally had, even if it converged to *something* > good. :) > -- > Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front > +358-40-3255353, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp > >
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