Consider an autoregressive system represented by a first-order difference equation
y[n] = 0.5y[n - 1] + x[n]
n >= 0
a. Find the impulse response h[n] of the system
b. Compute the response of the system to x[n] = u[n] - u[n - 3] using the convolution sum.
c. Verify results with MATLAB.
d. Determine the stability of the system using Matlab.