When the input to an LTI system is the output is (a) Determine the...

When the input to an LTI system is

the output is

(a) Determine the system function H(z) of the system. Plot the poles and zeros of H(z), and indicate the ROC.

(b) Determine the impulse response h[n] of the system for all values of n.

(c) Write the difference equation that characterizes the system.

(d) Is the system stable? Is it causal?