A causal linear time-invariant 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 region of convergence 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

(1 1.5z- z-2)(1 +0.9z-') (1 2-')(1 + 0.7jz-!)(1 0.7jz-) H(z) =