A causal LTI system has the system function (a) Write the difference equati...

A causal LTI system has the system function

(a) Write the difference equation that is satisfied by the input and the output of the system.

(b) Plot the pole–zero diagram and indicate the ROC for the system function.

(c) Sketch |H(e^jω)|.

(d) State whether the following are true or false about the system:

(i) The system is stable.

(ii) The impulse response approaches a constant for large n.

(iii) The magnitude of the frequency response has a peak at approximately ω = ±π/4.

(iv) The system has a stable and causal inverse.