IIRC, when I implemented Olli's coefficients I was seeing about 40dB image rejection. My optimized filter gave more like 58dB.
Eric On Feb 4, 2017, at 7:25 PM, robert bristow-johnson wrote: > > sunuvubych Olli. i shoulda known about this. > > i dunno Eric, 2/100 radian is about ±0.5°. that's what Olli is indicating on > Figure 3. appears to be an 8th-order using 4 pole pairs about the origin on > the real line. (i'm just now groking his design methodology.) and he seems to > have exceedingly low amplitude variation in the Analytic Filter magnitude > response. dunno what is lackluster about that. (but i haven't checked this > out, yet.) > > i know that because you can sorta treat group delay (which is a function > solely of phase) like gain in an all-pass filter, for the purposes of optimal > filter design technique (like Parks-McClellan or Prony). maybe that's what > Olli is doing. > > > -- > > r b-j r...@audioimagination.com > > "Imagination is more important than knowledge." > > > > ---------------------------- Original Message ---------------------------- > Subject: Re: [music-dsp] ± 45° Hilbert transformer using pair of IIR APFs > From: "Eric Brombaugh" <ebrombau...@cox.net> > Date: Sat, February 4, 2017 8:55 pm > To: music-dsp@music.columbia.edu > -------------------------------------------------------------------------- > > > The original Csound source has a set of coefficients for this type of > > hilbert transform but they don't say how the coefficients were derived > > and the performance is fairly lackluster. The only reference I've come > > across for this was Olli Niemitalo's: > > > > http://yehar.com/blog/?p=368 > > > > He gives a bit of theory, but the filter pair he provides doesn't give > > great performance. > > > > I was able to use Olli's filter as a starting point for optimization of > > a higher order AP set that gave almost 20dB better image rejection. I > > interpolated the originals to a higher order and then used simulated > > annealing with a cost function that included the bandwidth and image > > rejection. Rather brute-force, but it worked. > > > > Eric > > > > > > On 02/04/2017 04:32 PM, robert bristow-johnson wrote: > >> hey guys, > >> > >> what's the best online reference you can tell me for theory and practice > >> of designing APF pairs with ± 45° phase (+ a linear phase that > >> represents causality delay) to result in a Hilbert pair for audio > >> processing. i know how to do this for FIR and to use half-band > >> symmetry, but i wanna make a MATLAB program where i can specify order > >> and come up with an optimal pair of IIR APFs that have virtually 90° > >> phase difference over the widest possible frequency range. also some > >> discussion of error metric would be good (how do we decide what is > >> "optimal"?). eventually, i wanna compare computational effort with the > >> half-band FIR Hilbert transformer. > >> > >> anyone have a good, definitive reference? > >> > >> thanks. > >> > >> -- > >> > >> r b-j r...@audioimagination.com > >> > >> "Imagination is more important than knowledge." > >> > >> > >> > >> _______________________________________________ > >> 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 > > > > > > _______________________________________________ > 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
