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linear time-invariant discrete-time system and Matlab codes

A linear time-invariant discrete-time system has transfer function
h(z)=((z^2)-z-2)/((z^2) + 1.5z-1)

a. Use MATLAB to obtain the poles of the system. Is the system stable?
b. Compute the step response. This should be done analytically, but you can
use MATLAB commands like conv and residue.
c. 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?

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Solution Summary

The solution explains how to find the step response of a linear time invariant discrete system both analytically and in Matlab. It also includes the calculation of poles of the system in Matlab. Furthermore, the stability of the system is discussed.