Re: unwrapped phase and zeros

On Dec 14, 1:32 pm, "Ron N." <rhnlo...@xxxxxxxxx> wrote:
On Dec 14, 3:34 am, "rich_158" <eecod...@xxxxxxxxxxx> wrote:

hi
i am working on the group delay of speech signals and find that the signal
is very noisy when there are too many zeros of the z transform signal
around the unit circle resulting in too many phase jumps in the resulting
phase function. Why do zeros on the unit circle affect the unwrapped
phase so?

I am not sure why this is but find an explanation that:
The degree (no of 2 pi's) of wrapping in between two adjacent freq. points
around a zero depends on the closeness of the zero to the unit circle

can anyone clear this up for me?
cheers

Something sounds strange about the last statement. A zero
near the unit circle should cause a phase shift of around
pi radians as the frequency point on the unit circle goes
past that zero by an amount much greater than the distance
to that zero. For increasing frequency, the phase should
increase for a nearby zero slightly inside the unit circle,
and decrease for a nearby zero slightly outside the unit
circle. The nearness of the zero to the unit circle should
mostly affect the peak rate or slope of the phase change,
much less so the total amount of phase change.

Another item that might be useful to keep the phase continuous
is to use a few modified versions of the atan() function, so
that the angle/phase result remains continuous over the domain
being examined. For instance, for poles or zeros outside the
unit circle and in the upper half of the complex plane, one
would use an atan() that ranges from -3*pi/2 to pi/2, so that
the angle to it will never wrap as one traverses the unit
circle, since the unit circle will never be above that pole or
zero. For positive frequencies, two different versions of
atan() might be required: one for poles/zeros outside and
upper, and one for those inside the unit circle or in the
lower half of the complex plane.



IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
http://www.nicholson.com/rhn/dsp.html
.

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