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From: Jerry Avins on 8 Aug 2010 12:25
On 8/8/2010 9:22 AM, jungledmnc wrote:
> Damn it, sorry for my last post, it was a bug, I accidentally added a 1
> sample delay to one channel... Such a stupid mistake...

Congratulations on a job well done. Now that you have an answer, to the
symmetries become apparent?

Jerry
--
Engineering is the art of making what you want from things you can get.
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From: Vladimir Vassilevsky on 8 Aug 2010 12:50


Angelito Hamm wrote:

> On Aug 6, 5:33 pm, "jungledmnc" <jungledmnc(a)n_o_s_p_a_m.gmail.com>
> wrote:
>
>>Hi,
>>I want to create a frequency shifter for audio. First I need to get an
>>analytical signal via a hilbert transformer. I started by checking out how
>>long the Hilbert FIR would be. Unfortunately I ended with 20ms, which seems
>>to be related to -3dB at 50Hz (1/0.02). Isn't there another way to do that?
>>I mean 20ms is a relatively long delay for realtime processing and also 800
>>taps would need relatively lots of CPU power.
>>
>>Thanks.
>
>
> A detailed description of the pole-zero rotation approach to analytic
> signal generation using IIR described by Dr. Brackett in this thread
>
> http://groups.google.com/group/comp.dsp/msg/08d2545fde320d54?dmode=source
>
> is published in
>
> Vanbeylen, L. Schoukens, J.
> "Comparison of Filter Design Methods to generate Analytic Signals"
> Instrumentation and Measurement Technology Conference, 2006. IMTC
> 2006. Proceedings of the IEEE
> 24-27 April 2006
> pp. 883 - 887


It is possible to make a Hilbert filter approximation by Greg Berchin's
FDLS method as well. The result of FDLS could be further optimized
numerically; this allows for making very efficient filters with
non-standard structure.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com


From: jungledmnc on 8 Aug 2010 15:35
Thank you people for your help. My "numerical" method is quite "simple"
indeed :), but it seems working well, and that's important!

Cheers!
From: robert bristow-johnson on 8 Aug 2010 22:53
On Aug 8, 9:02 am, "jungledmnc" <jungledmnc(a)n_o_s_p_a_m.gmail.com>
wrote:
> >On Aug 7, 8:24=A0pm, "jungledmnc" <jungledmnc(a)n_o_s_p_a_m.gmail.com>
> >wrote:
> >> I take it there is no simple way to compute the
> >> allpass coefficients, except for brute-force search. So I did it.
>
> >exactly what?  how did you search for your optimal coefs and what did
> >you get?
>
> >> I wrote a simple app, which searches for requested number of allpass
> >> sections evaluating results like this:
>
> >> H1 = Hallpass_A1(z) * Hallpass_A2(z) * ..
> >> H2 = Hallpass_B1(z) * Hallpass_B2(z) * ..
> >> where everything is complex. |H1| = |H2| = 1 as expected.
>
> >> Finally phase1 = atan2(H1.R,H1.I) + PI/2, phase2 = atan2(H2.R,H2.I)
> >> Difference = phase1 - phase2, and some wrapping.
> >> Difference should be as close to 0 as possible.
>
> >difference should be close to 0 or close to pi/2?
>
> The PI/2 was added to phase 1 (above).

okay, i see that now.

so then, is phase2 reasonably close to linear phase (a constant delay)
or does that not matter? maybe a better question is if

arg{H1} + pi/4

arg{H2} - pi/4

are sufficiently phase linear? just getting them to differ by pi/2
over a wide range of frequencies is an accomplishment (i would still
like to see the APF coefficients) and will work for a frequency
shifter, but if the residual phase is not very linear, it's like you
passed the signal through an all-pass filter that is not a simple
delay line before shifting the frequency.

> I did it simply by random walk :) - random parameters repeatedly until it
> finds some "a little good" solution, then moving the parameters randomly a
> little searching for better solution.
>
> The question is more like, if I multiply the H(z) of each stage and take
> its phase, should it represent the resulting phase shift? Or could there
> be a problem with the measurement by taking an impulse and FFTing the
> output?

you should be able to do both and get comparable results.
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