Re: the polar and zero of frequency response

On May 13, 4:20 am, HyeeWang <hyeew...@xxxxxxxxx> wrote:
In such LTI system equation, the polar points make the amplitude of
transfer function to be infinite, and in contrast to that, the zero
points make it to be zero.

But from the frequency response figure which is ploted by matlab freqz
function, I can not get such a view.

Let we assume that, say a ordinary example, there are 4 conjugated
zero points in the angle pi/10 and 3*pi/10, and
there are 4 conjugated pole points in the angle 5*pi/10 and 7*pi/10. I
plot its frequency response with matlab.

To my surprise,I can not see what I expected,which is : there should
be 2 notches and 2 overshoots in the location 0.1,0.3,0.5 and 0.7,at
the magnitude plot of frequency response.

Why? Where it go wrong? I know the ampltidute plot is in DB sense.

Here is the attached matlab scripts to illustrate it.

r1=0.5;
r2=0.8;
r3 = r1;
r4 = r2;

th = pi/10;

z1 = r1*exp(j*th);
z2 = r2*exp(j*th*3);
z3 = r3*exp(j*th*5);
z4 = r4*exp(j*th*7);

% z = [z1,z2,z3,z4];
% plot(z,'*');

b = poly([z1,conj(z1),z2,conj(z2)]);
bz = roots(b);

a = poly([z3,conj(z3),z4,conj(z4)]);
az = roots(a);

freqz(b,a);

Any comments would be appreciated.

Cheers
HyeeWang

Freqz evaluates the response on the unit circle. Your poles
and zeros are not on the unit circle.

You should read up on what freqz exactly does ....
.

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