Hilbert Transform Phase

On Apr 23, 11:41&#4294967295;am, Dirk Bell <bellda2...@cox.net> wrote:
> On Apr 23, 11:17&#4294967295;am, Clay <c...@claysturner.com> wrote:
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> > On Apr 22, 6:27&#4294967295;pm, Dirk Bell <bellda2...@cox.net> wrote:
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> > > On Apr 22, 5:42&#4294967295;pm, Jerry Avins <j...@ieee.org> wrote:
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> > > > On 4/22/2010 2:26 PM, Dirk Bell wrote:
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> > > > > On Apr 16, 1:26 am, Jerry Avins<j...@ieee.org> &#4294967295;wrote:
> > > > >> On 4/16/2010 12:43 AM, cfy30 wrote:
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> > > > >>> Hi all,
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> > > > >>> I am a newbie to Hilbert transform. I found the follow definition from
> > > > >>> textbook
>
> > > > >>> H(f) = -j or -90degree, f>0
> > > > >>> H(f) = &#4294967295;j or +90degree, f<0
> > > > >>> H(f) = &#4294967295;0, f=0
>
> > > > >>> But when I plot the phase out in Matlab, I saw that the phase is not
> > > > >>> constant at -90 or +90degree across frequency. The code I have is as
> > > > >>> follow
>
> > > > >>> b = firpm(10,[.1 .9],[1 1],'Hilbert')
> > > > >>> w = linspace(-pi, pi, 2^12);
> > > > >>> h = freqz(b, 1, w);
> > > > >>> plot(w, angle(h)*180/pi);
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> > > > >>> What do I miss?
>
> > > > >> The phase is 90 degrees only over a limited band. All bets are off at
> > > > >> Fs/2, and you can't include enough taps to get 90 degrees of delay at
> > > > >> DC. What's more, there will be some amplitude ripple in the passband.
> > > > > Jerry,
>
> > > > > The phase is not really 90 degrees only over a "limited" band. &#4294967295;Try a
> > > > > 100K point FFT on the OP's filter (remove delay) and the only 2 values
> > > > > that are not +-pi/2 with error magnitude<4*10^-13 radians are at 0
> > > > > and pi radians where they are zero. &#4294967295;The phase is essentially correct
> > > > > over the whole band. &#4294967295;The amplitude is another story.
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> > > > Dirk,
>
> > > > Of course you're right. Antisymmetry assures that the phase be perfect
> > > > even with a balanced differentiator, [-1, 0, +1]. I had in mind the
> > > > implementation with parallel filters whose difference approximates 90
> > > > degrees over the bans of interest. Bad form!
>
> > > > Jerry
> > > > --
> > > > "It does me no injury for my neighbor to say there are 20 gods, or no
> > > > God. It neither picks my pocket nor breaks my leg."
> > > > &#4294967295; &#4294967295; &#4294967295; &#4294967295; &#4294967295; Thomas Jefferson to the Virginia House of Delegates in 1776.- Hide quoted text -
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> > > > - Show quoted text -
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> > > Hi Jerry,
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> > > I took my post down because I looked at later posts and thought it was
> > > basically covered. &#4294967295;However antisymmetry by itself is not enough to
> > > guarantee perfect phase. &#4294967295;For example [1 &#4294967295; &#4294967295; 0 &#4294967295; &#4294967295;-1 &#4294967295; &#4294967295; 0 &#4294967295; &#4294967295; 1
> > > 0 &#4294967295; &#4294967295;-1] does not work.
>
> > > I was curious about another comment somone here made. &#4294967295;What is the
> > > best way to design a 45 degree phase shifter?
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> > > Dirk- Hide quoted text -
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> > > - Show quoted text -
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> > I don't know if it is the best way, but it is a simple way. &#4294967295;See:
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> >http://www.claysturner.com/dsp/ASG.pdf
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> > Clay- Hide quoted text -
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> > - Show quoted text -
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> Thanks Clay.
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> Dirk- Hide quoted text -
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> - Show quoted text -

You are welcome.

On 4/23/2010 8:17 AM, Clay wrote:
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 > [snip]
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> I don't know if it is the best way, but it is a simple way.  See:
>
> http://www.claysturner.com/dsp/ASG.pdf
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>
> 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

On Apr 23, 12:12&#4294967295;pm, Rob Gaddi <rga...@technologyhighland.com> wrote:
> On 4/23/2010 8:17 AM, Clay wrote:
>
>
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> &#4294967295;> [snip]
>
> > I don't know if it is the best way, but it is a simple way. &#4294967295;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