Question

Plot the first seven values of the step response. Is the response increasing or decreasing with time? Is this what you would expect, and why?
H(z)= (z^2-z-2)/(z^2+1.5z-1)

I calculated the step response to be
y(n)= (0.5333(-2)^n+1.3333+1.8(0.5)^n)u[n]

In the plot, half of the points increasing and the other half decreasing. Is this correct because of the unstable system?  

Thanks

Answer 1

clc
clear all
close all
n=0:7;
y=(0.5333*(-2).^n+1.333+1.8*(0.5).^n);
stem(n,y)
title('Step Response')
xlabel('Number of samples')
ylabel('Amplitude')

clc
clear all
close all
n=0:20;
y=(0.5333*(-2).^n+1.333+1.8*(0.5).^n);
stem(n,y)
title('Step Response')
xlabel('Number of samples')
ylabel('Amplitude')

The system is unstable because as n increase the response tends to infinity.

The condition for stability is as n--> infinity, sum of (|h(n)|)<infinity. or The system should be absolutely summable.

Here because of (-2)^n the system becomes unstable because as n increase the values increase by its power.

And the negative sign give +ve and -ve values in the response.