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# linear time-invariant continuous system and Matlab

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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).