Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively. poles and zeros define the performance of a system.

1. Discrete Time Signal Processing Lab
1
Q1. Find the transfer function? Plot poles, zeros on z-plane?
MATLAB code
clc
clear all
close all
%Q1
P1=[1/3; 2; 3]; %poles
Z1=[-1]; %zeros
figure(1);
zplane(Z1, P1) %pole-zero plot command
[num1, den1]=zp2tf(Z1, P1, 1); % get num denum of transfer function
TF1=filt(num1,den1) % gives the transfer function,
Output
Q2. Poles and zeros are given, poles are complex. Plot poles, zeros on zplane. Find Transfer function?
MATLAB code
P2=[0.5j; -0.5j] ; %poles
Z2=[1/4];
figure(2)
zplane(Z2, P2)
[num2, den2]=zp2tf(Z2, P2, 1);
TF2=filt(num2,den2)

2. Discrete Time Signal Processing Lab
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Output
The output pole zero plot is shown in figure2 above. And we got Transfer function at command window,
it was..
Q3. Poles and Zeros are given. Zeros are complex values. Plot poles, zeros on z-plane. Find
transfer function?
MATLAB code
P3=[0.65];
Z3=[0.65 + 0.65j; 0.65-0.65j];
figure(3)
zplane(Z3, P3);
[num3, den3]=zp2tf(Z3, P3, 1);
TF3=filt(num3,den3)
Output

3. Discrete Time Signal Processing Lab
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MATLAB code
syms a x n
n=(0:120)
a1=0.6;
x1=a1.^n;
stem(n,x1)
a2=-3;
x2=a2.^n;
stem(n,x2)
a3=0.5*exp((pi/4)*j);
x3=a3.^n;
stem(n,x3)
%b part
num4b=[0 1]
denum4b=[1 -0.7]
freqz(num4b,denum4b)
denum4b2=[1 3]
freqz(num4b,denum4b2)
The respective output plots are shown below, mentioned with detailed title.

4. Discrete Time Signal Processing Lab
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5. Discrete Time Signal Processing Lab
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Part c of this question was much similar to the part b of Q5 while solving, so it is solved once for part b
os Q5. i.e same MATLAB commands are to be implemented.
MATLAB code
%a part
P5=[-1/4; 1/3];
Z5=[-1/3];
figure(5)
zplane(Z5, P5)

6. Discrete Time Signal Processing Lab
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Code for part b of Q5 is written below, its output is mentioned with label in
above figures.
%b part
[num5, den5]=zp2tf(Z5, P5, 1)
TF5=filt(num5,den5)
[Z5b,P5b,K] = tf2zp(num5,den5)
roots([ 1.0000; -0.0833; -0.0833])
MATLAB code
b. finding poles and zeros using roots command
code
zeros=roots([2; 2; 2])
poles=roots([2; -3; 1])
output
finding poles and zeros using tf2zp command, output at command window shown
below.

7. Discrete Time Signal Processing Lab
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a. Poles zeros plot using zplane command.
MATLAB code
P6=([1.00; 0.500])
Z6=([-0.5000 + 0.8660i; -0.5000 - 0.8660i])
Zplane(Z,P)
Engr. Arif Hussain
COMSATS Abbottabad,
Pakistan.