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).
The solution is comprised of detailed explanation of application of Laplace transform to find the transfer function of the linear time-invariant continuous system in s-domain. It also shows the calculation of the impulse response of the system. Furthermore, it also elaborates on finding the system output in both s-domain and time domain with certain input. Finally, the application is verified in Matlab codes.