2. System function of a discrete-time and causal LTI system has a zero at z = 0 and two poles at pi = 0.5e 7/4 and p2= 2e i 4. Write the system function H(z). a) Show zero, poles and ROC of this...

Extracted text: 2. System function of a discrete-time and causal LTI system has a zero at z = 0 and two poles at pi = 0.5e 7/4 and p2= 2e i 4. Write the system function H(z). a) Show zero, poles and ROC of this system on Z-plane. Is this system stable? Explain. b) Find the impulse response of the system. c) Give the input / output difference equation of the system. d) If the system is stable solve (a), (b), (c) again.