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

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