clc;
clear all;
close all;
f=input('enter the sine wave frequency f = ');
a=input('Enter the value of a= ');
n=0:0.5:20;
syms f n a;
x1=cos(2*pi*(f)*n).*exp(-a*n);
z = ztrans(x1);
pretty(z)
%Solves the Z transform equation
ZtranSolu = collect(z);
%Extracting numerator and denominator
[num,den] = numden(ZtranSolu);
num
den
ts = 0.9; % Sampling period
H = tf(sym2poly(num),sym2poly(den),ts)
% To plot the pole's and zero's of z transform
figure('name','Pole Zero Plot')
pzmap(H)
--------------------------------------------------------------------------
I am getting the following error
Error using sym/sym2poly
Not a polynomial.
Error in test
H = tf(sym2poly(num),sym2poly(den))
The stability criteria is based solely on the pole plot zero pole plot of the Laplace transform of the transfer function of system H(s). If H(s) contains poles in the right hand side of the s-plane, then the system will be unstable.
Alternatively if you have a system and you apply on it a sinusoidal wave and you get at the output a time growing sinusoidal wave then the system will be unstable. So, i can tell you directly whether your system is stable or not if i get such system response.
If a is positive then the cosine wave will decay and your system will be stable having the poles in the left hand side of the s-plane. If a is negative then the cosine will grow with time and the system will be unstable.
Converting to Z transform will not give you more information concerning the system stability.
You can find in the z transformation tables of the standard functions the function which you search for. The transformation contains one zero and two poles in the z-plane. For stable system, the two poles must lay inside the unity circle.
Best wishes
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