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?
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.
MATLAB Signals - Conv and Transfer Function of System
1. A discrete-time system has the following unit-pulse response:
h[n] = 0.5^n - 0.25^n for n >= 0
Correspondingly, the following difference equation describes the behavior of the system:
y[n + 2] - 0.75y[n +1] + 0.125y[n] = 0.25x[n +1]
a. Use the MATLAB command conv to calculate the response of the system
to a unit step input, x[n]=u[n]. Consider 0 <= n <= 20 . Show what you type into the MATLAB command window. Also, submit a plot of the output. Be sure to label your axes.
2. A linear time-invariant continuous-time system has the impulse response below:
h(t) =[cos 2t + 4 sin 2t]u(t)
(a). Determine the transfer function H(s) of the system.
(b). Plot the system impulse response using MATLAB.
(c). The input, x(t) is defined as x(t)=((5/7)e^-t) - ((12/7)e^-8t), x >= 0. Find x(s).
(d). Compute the output response Y(s).
(e). Compute and plot y(t).