Use MATLAB to generate a random sequence x[n] for n = 0, 1, ..., 99 and set x[n] = 0 for n < 0 and n > 99. (a) Consider a discrete-time LTI system with the impulse response h[n] = 0.9^n u[n] and the output y[n] = h[n]* x[n]. Compute and plot the output y[n] for n = 0, 1, ..., 200 using the convolution sum. (b) Consider another discrete-time LTI system governed by the recursive difference equation y[n] = 0.9y[n - 1] + x[n] and the initial condition y[-1] = 0. Compute and plot the output y[n] for n = 0, 1, ..., 200 using the recursive equation (c) Compare and discuss the two outputs above. Are they the same? Why or why not?
