Consider an LTI (linear time-invariant) system whose impulse response h[n] and input signal x[n] are given as:

h[n] = u[n-2]

x[n] = (1/2)^n u[n-4]

Find the output y[n] of the system for all values of n. Show every step of your work, making sure to label the axes, as well as any important points/values in your graphs.

A plot of x[n] and h[n] gives the plot of the graph.

Explanation:

The impulse responses are depicted by suitable diagrams.

The output of the system will be the sum total of the response to the signal h[0], h [1] and h [2].

Thus, the three signals will be:

h[0]x[n] = 3x[n]

h[1]x[n] = 3x[n-1]

h[2]x[n-2] = x[n-2]

Therefore, the output of the system will be like this:

y[n] = [ 0, 0, 3, 6, 7, 7, 4, 1, 0, 0]