FPGA Central

Hi all,
I still have difficulties with this type of questions:
Know the H(z), I find zeros and poles. Now they require I plot a rough
sketch of |H(omega)|.

plz guide me any webpages or books where they discuss/teach about it? I
think it is taught at the basic level, but unfortunately I have never
leant it .

Thanks

in article [email protected] com,
[email protected] at [email protected] wrote on 09/23/2005 22:03:

> I still have difficulties with this type of questions:
> Know the H(z), I find zeros and poles. Now they require I plot a rough
> sketch of |H(omega)|.

this has been done before, but i can't find the post in Google groups.

what you are asking for is |H(e^(j*omega))| where H(z) is the z transform of
your impulse response (otherwize known as the "transfer function"). i'm
gonna call it |H(e^(j*w))| where "w" is pronounced "omega".

if

(z-q1)*(z-q2)*...
H(z) = A -------------------
(z-p1)*(z-p2)*...


then



(e^(j*w)-q1)*(e^(j*w)-q2)*...
H(e^(j*w)) = A -------------------------------
(e^(j*w)-p1)*(e^(j*w)-p2)*...



and


|e^(j*w)-q1|*|e^(j*w)-q2|*...
|H(e^(j*w))| = |A| -------------------------------
|e^(j*w)-p1|*|e^(j*w)-p2|*...


so, given some value of "omega" where 0 <= w <= pi, the complex number
e^(j*w) is on the unit circle at an angle of w, right? so you know where
that point is graphically as well as the locations of your poles and zeros,
right?

so then you take the magnitude of the constant A, multiply by |e^(j*w)-q1|
which is the distance e^(j*w) is from the zero q1, repeat with q2 and q3 and
the rest of the zeros. do the same for the p p1 and p2 etc, but for the
poles, you *divide* by the distance e^(j*w) is from the pole p1 or p2 or p3,
etc.

so, imagine you're sitting on top of e^(j*w) as you go around the unit
circle, as you get closer to a zero, the distance to that zero decreases and
|H(e^(j*w))| decreases. as you get closer to a pole, the distance to that
pole decreases but |H(e^(j*w))| INcreases.

that's it. can you have learnt it now?


--

r b-j [email protected]

"Imagination is more important than knowledge."

VijaKh...@gmail.com wrote:
> Know the H(z), I find zeros and poles. Now they require I plot
> a rough sketch of |H(omega)|.

Depends how rough. At the roughest level, walk around the unit
line or circle: there's a hump if you're near a pole and a dip
if you're near a zero. The closer you are to a pole or zero,
the bigger the hump or dip on the path (max/min at infinity or
zero if you encounter one directly on your path). If there
is an equidistant pole/zero pair, then their effects cancel
and the path stays flat exactly between them. If there are
lots of poles and zeros, take all the effect of each one and
multiply them out to see how hilly your path looks. Roughly.

If you want a 3d true-color hidden-surface texture-mapped plot
while animating the poles and zeros around a path that spells
your full name in cursive and simultaneously spinning the axis
and zooming your viewpoint in and out in real time until you
are dizzy, the are probably software packages that can do that.


IMHO. YMMV.
--
Ron
rhn A.T nicholson d.O.t C-o-M

as you go up in frequency on a bode plot

a pole causes a break point downwards at -6 dB per octave


and a zero causes a breakpoint upwards at +6 dB per octave.

Mark