How to see the freq response of a transfer function

I am having Transfer Function

H(z)= .5z(2)+1/ [z(2)+1]

i want to plot its freq response using omega axis

Answer 1

[Wayne King]

Hi, I'm going to assume that by z(2) you mean z^{-2}.

You can do a couple things.

[H,W] = freqz([1 0 0.5],[1 0 1]);
plot(W,20*log10(abs(H)));
set(gca,'xlim',[0 pi]); grid on;
xlabel('Radians/sample');

Or

    fvtool([1 0 0.5],[1 0 1]);

Answer 2

[moonman]

Hi King thanks a lot. I am stuck with this multiple choice of book Can u help me and see it. As per ur direction, i checked the freq response and as per my responses, option (a) is correct

Can u just cross check my answer thanks a lot

http://www.4shared.com/photo/GiQkD_CP/Query.html

[Wayne King]

Hi, I don't think that is correct. If you look at the pole-zero plot for that

zplane([0.5 0 1],[1 1]);

That frequency response peaks near pi radians/sample or 1 in omega/pi.

You have a lowpass filter in your figure.

Answer 3

[moonman]

Can u kindly suggest which one is correct I have plotted all four responses and only this response is having matching shape with that of given figure

Any idea which one is correct

[Wayne King]

I know which one is correct, but I don't want to just give you the answer. You have to keep in mind that

[H,W] = freqz(....) is giving you zero frequency first. Your book is plotting zero frequency in the middle. That may be confusing you. What is the value of your transfer function at zero frequency?

Look at H(1) for you possibilities that is the transfer function at 0 frequency.

Answer 4

[Wayne King]

Also, you see that your plotting frequency response has zero as 0-1j and 0+1j. That means there are zeros on the unit circle at those frequencies (angles).

Use

zplane(B,A)

to look for those zeros.

Answer 5

[moonman]

thanks for finishing this confusion

for H(1) at zero i m having magnitude of about -3 db

So answer (b) is correct choice b/c at zero freq, it is having arount 18 db which comes to be 64 and at freq of 1, it is having around 1 db which comes to be 1.25

I think the book has drawn it to 80 by mistake

So am i correct in saying (b) is correct option

thanks for guiding me

[moonman]

Ur this guidance zplane(B,A)

also confirms that (b) is correct choice

[Wayne King]

You're right.

They are just plotting the magnitude, so at zero frequency they have 8.

Look at:

[H,W] = freqz([1 0 1],[1 -0.75]);

H(1)

Answer 6

[moonman]

I also changed the scale to decimal Analysis Parameter and now i am 100% sure. thanks a lot King

Can u lastly explain me that how u came to know by seeing that my plotting frequency response (book figure) has zero as 0-1j and 0+1j

I also want to be know it

Great help by u

[Wayne King]

Because I saw that the magnitude was zero at -0.5 and 0.5, which corresponds to angles of -pi/2 and pi/2

exp(1j*pi/2) = 0+1j

exp(-1j*pi/2) = 0-1j

Answer 7

[moonman]

Wayne King thanks a lot, ur explanation is always wonderful and u make me understand the whole topic.

U r Excellent Expert. Hats Off for u