Unit circle and location of zeros ...

I need to solve the following problem:
I was given frequency response of some FIR filter, consisting
of two plots Magnitude response and Phase response.

- From Magnitude response plot I can easily identify number and
polar angles of zeros. There are 5 zeros in my case. One of them
located on the unit circle.

- From Phase response plot I can see that filter is mixed phase,
which means that some zeros are inside unit circle and others are
outside.

Here is my question: How can I find out what zeros are located
inside unit circle and what are outside unit circle? Please
remember that I don't have any other information about this filter
besides these two plots.

Thanks in advance

Bobby wrote:
> I need to solve the following problem:
> I was given frequency response of some FIR filter, consisting
> of two plots Magnitude response and Phase response.
> 
> - From Magnitude response plot I can easily identify number and
> polar angles of zeros. There are 5 zeros in my case. One of them
> located on the unit circle.
> 
> - From Phase response plot I can see that filter is mixed phase,
> which means that some zeros are inside unit circle and others are
> outside.
> 
> Here is my question: How can I find out what zeros are located
> inside unit circle and what are outside unit circle? Please
> remember that I don't have any other information about this filter
> besides these two plots.
> 
> Thanks in advance

Sounds like homework -- but everything on this list sounds like homework.

If I _knew_ that there were exactly 5 zeros (how?), and I _knew_ their 
locations, I'd look at the phase plot for the direction that the phase 
is breaking.

Whether I did the above or not, I'd do a curve fit of the measured data. 
  Since you know you have all zeros (how?) you can do linear regression on

a_5 + a_4/e^jw + a_3/e^j2w + etc

against your measured data to get the coefficients, check for goodness 
of fit, then take the roots of the polynomial a_5 z^5 + ... + a_0 for 
your zero locations.  If linear regression doesn't work then you can 
just use zero locations directly, but finding the global minimum is up 
to you.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Yes, you are right. It is homework ...

>> If I _knew_ that there were exactly 5 zeros (how?), ...<<
In my case I was able easily identify that there are 5 zeros just by
looking into magnitude plot. I was able clearly see at what polar
angles they are.
The only thing I didn't understand is whether they are inside or
outside unit circle.

>>and I _knew_ their  locations<<
If I knew their exact location I wouldn't ask this question ...

Thanks

Tim Wescott <tim@wescottnospamdesign.com> wrote in message news:<10okloh594mm948@corp.supernews.com>...
> Bobby wrote:
> > I need to solve the following problem:
> > I was given frequency response of some FIR filter, consisting
> > of two plots Magnitude response and Phase response.
> > 
> > - From Magnitude response plot I can easily identify number and
> > polar angles of zeros. There are 5 zeros in my case. One of them
> > located on the unit circle.
> > 
> > - From Phase response plot I can see that filter is mixed phase,
> > which means that some zeros are inside unit circle and others are
> > outside.
> > 
> > Here is my question: How can I find out what zeros are located
> > inside unit circle and what are outside unit circle? Please
> > remember that I don't have any other information about this filter
> > besides these two plots.
> > 
> > Thanks in advance
> 
> Sounds like homework -- but everything on this list sounds like homework.
> 
> If I _knew_ that there were exactly 5 zeros (how?), and I _knew_ their 
> locations, I'd look at the phase plot for the direction that the phase 
> is breaking.
> 
> Whether I did the above or not, I'd do a curve fit of the measured data. 
>   Since you know you have all zeros (how?) you can do linear regression on
> 
> a_5 + a_4/e^jw + a_3/e^j2w + etc
> 
> against your measured data to get the coefficients, check for goodness 
> of fit, then take the roots of the polynomial a_5 z^5 + ... + a_0 for 
> your zero locations.  If linear regression doesn't work then you can 
> just use zero locations directly, but finding the global minimum is up 
> to you.