Locating the zeros and poles and plotting the pole zero maps in zplane for the given transfer function
Aim: To locating the zeros and poles and plotting the pole zero maps in zplane for the given transfer function
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
Theory: The Ztransform converts a discrete timedomain signal, which is a sequence of real or complex numbers, into a complex frequencydomain representation.The Ztransform, like many other integral transforms, can be defined as either a onesided or twosided transform.
Bilateral Ztransform
The bilateral or twosided Ztransform of a discretetime signal x[n] is the function X(z) defined as
Unilateral Ztransform
Alternatively, in cases where x[n] is defined only for n = 0, the singlesided or unilateral Ztransform is defined as
In signal processing, this definition is used when the signal is causal.
The roots of the equation P(z) = 0 correspond to the 'zeros' of X(z)
The roots of the equation Q(z) = 0 correspond to the 'poles' of X(z)
The ROC of the Ztransform depends on the convergence of the
Program1: plotting poles and zeros on zplane
clc;
close all
clear all;
%b= input('enter the numarator cofficients')
%a= input('enter the dinomi cofficients')
b=[1 2 3 4]
a=[1 2 1 1 ]
zplane(b,a);
Output:
Applications :ZTransform is used to find the system responses
Program2: plotting poles and zeros on zplane
clc;
clear all; close all;
num=input('enter the numerator polynomial vector \n'); %[1 0 0]
den=input('enter the denominator polynomial vector \n'); %[1 1 0.16]
H=filt(num,den)
z=zero(H);
disp('the zeros are at ');
disp(z);
[r p k]=residuez(num,den);
disp('the poles are at ');
disp(p);
zplane(num,den);
title('PoleZero map in the Zplane');
if max(abs(p))>=1
disp('all the poles do not lie with in the unit circle');
disp('hence the system is not stable');
else
disp('all the poles lie with in the unit circle');
disp('hence the system is stable');
end;
OUTPUT:
Enter the numerator polynomial vector
[1 0 0]
Enter the denominator polynomial vector
[1 1 0.16]
Transfer function:
1

1 + z^1 + 0.16 z^2
The zeros are at
0
0
The poles are at
0.8000
0.2000
All the poles lie with in the unit circle
Hence the system is stable
Result: In this experiment the zeros and poles and plotting the pole zero maps in splane and zplane for the given transfer function using MATLAB.
Viva Questions:
1.what are the ROC properties of a Z.T
Ans: a1 x1[n] + a2 x2[n] = a1 X1(z) + a2 X2(z)
2.Define Initial Value Theorem of a Z.T
Ans:
if x(n] is casual
3. Define Final Value Theorem of a Z.T
Ans:
Only if poles of (z1)X(z) are inside the unit circle
4. Define the condition for distortionless transmission through the system
Ans: Transmission is said to be distortion less if the input and output have identical wave shapes within a multiplicative constant.A delayed output that retains the input waveform is also considered distortion less.Thus in distortionless transmission, the input x(t) and output y(t) satisfy the condition:y(t) = Kx(t  t) where t is the delay time and k is a constant

UpdatedMar 01, 2020

Views2,728
Sampling theorem verification
Finding the even and odd parts of signal/sequence and real and imaginary parts of signal
Genaration of various signals and sequences
Auto correlation and cross correlation between signals and sequences
Computation of unit sample, unit step and sinusoidal response of the given LTI system and verifying its physical reliability and stability properties
Basic operations on Matrices