Hilbert Transform Phase
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From: Rob Gaddi on 23 Apr 2010 12:12 On 4/23/2010 8:17 AM, Clay wrote: > > [snip] > > I don't know if it is the best way, but it is a simple way. See: > > http://www.claysturner.com/dsp/ASG.pdf > > > Clay > Clay, I'm holding you personally responsible for the fact that I'm sitting here trying to get my head around this paper instead of doing my actual, entirely un-Hilbert-transform-related, job. -- Rob Gaddi, Highland Technology Email address is currently out of order
From: Clay on 23 Apr 2010 12:32 On Apr 23, 12:12 pm, Rob Gaddi <rga...(a)technologyhighland.com> wrote: > On 4/23/2010 8:17 AM, Clay wrote: > > > > > [snip] > > > I don't know if it is the best way, but it is a simple way. See: > > >http://www.claysturner.com/dsp/ASG.pdf > > > Clay > > Clay, I'm holding you personally responsible for the fact that I'm > sitting here trying to get my head around this paper instead of doing my > actual, entirely un-Hilbert-transform-related, job. > > -- > Rob Gaddi, Highland Technology > Email address is currently out of order Sorry about the destraction ;-) It should get you to think about vectors and rotations. You know how much I like matrices ;-) Clay
From: Robert Orban on 21 Apr 2010 19:57
In article <Xs6dnbGFup7rZ1rWnZ2dnUVZ_t-dnZ2d(a)giganews.com>, steveu(a)n_o_s_p_a_m.coppice.org says... > >Just a few terms for an FIR implementation of a Hilbert transform can give >you pretty close to 90 degrees over a large part of the band. Don't expect >a perfect brick wall transition from + to - 90 at DC, though. Its the >amplitude response that is the greater problem. It takes a lot of terms to >get that close to flat at low and high frequencies. IIRC, as long as the impulse response of the FIR is stictly antimetric around the center tap, you will have an exact 90 degree phase shift (+ a fixed delay) at all frequencies regardless of the number of taps. (A trivial example is a three-tap filter whose impulse response is -1, 0, +1.) The problem, as other posters have commented, is that for a given amplitude passband bandwidth, low-order FIR filters have larger amounts of amplitude ripple in the filter passband than higher-order filters and no filter with a finite number of taps can have an ampltude bandwidth extending from DC to fs/2. It is possible to transform the filter structure such that the amplitude response is flat but the phase shift error varies over the passband. What is not possible with a finite number of taps is to obtain a flat passband from 0 to fs/2 Hz and a 90 degree phase shift (+ fixed delay) simultaneously. |