Re: pole zero stuff


"richard pickworth" <richard.pickworth@xxxxxxxxxxxxxxx> wrote in message
news:dcaolt$2bd$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Hi all.
> I am confused about pole - zero diagrams and how they relate to filter
> response.
> Also confused about unit circle and IIR filters.
> Can anyone help?
> yours
> Richard

Richard,

If you're visually oriented then you may like this:

Plot the poles and zeros in the s-plane or the z-plane.
Imagine that the plane is covered flat with an elastic ***.
Imagine that there is a thumb tack holding the *** down at the location of
each zero.
Imagine that there is a pencil holding the *** up from the plane at the
location of each pole.
Now, really, the poles would be of infinite height so you need to do a bit
of visualization there.
The resulting surface approximates the shape of the magnitude over the
plane.

Now, visualize how the surface of the *** varies if you traverse the jw
axis in the s-plane or the unit circle in the z-plane.
If there are zeros on the unit circle then the height of the *** is zero.
If there are poles near the unit circle then the height of the *** is
affected as well.

Imagine one pole in the z-plane at the orgin - the entire *** is lifted
and the height above the unit circle is uniform.
Now, put one zero at fs/2 or pi on the unit circle. The entire ***
remains above the plane over the unit circle except at pi where it's at zero
height.

It's not as good as using more careful plots but it can be useful in
thinking about how certain filters work.

Fred


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