� you know it's embarrassing to rediscover you've been somewhere before, after totally forgetting about it. so Olli, how do you get your coefficients? �(if i may ask?) r b-j� ---------------------------- Original Message ---------------------------- Subject: Re: [music-dsp] � 45� Hilbert transformer using pair of IIR APFs From: "robert bristow-johnson" <r...@audioimagination.com> Date: Sat, February 4, 2017 9:25 pm To: music-dsp@music.columbia.edu -------------------------------------------------------------------------- > > > > � > 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
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