Problem #2 (30 points)
Consider a discrete-time LTI system with input x[n] and output y[n], described by the following difference equation:
y[n] - y[n-1] = x[n] + x[n-1]
a. (5 pts) Determine the transfer function, H(z), for this system.
b. (5 pts) Determine the locations of the poles and zeroes, and plot them in the z-plane.
c. (6 pts) Draw the possibilities for the region of convergence (ROC).
d. (10 pts) Derive the impulse responses, h[n], for each of the ROCs determined in b.
e. (4 pts) Can this system be both causal and stable? Explain.
z - Y^2 - 2 = Y^2X + 2^2fX^2
Hca Yo x^2
2^12
Poles: 7
Zeroes: Gl
