We want to design a causal discrete-time LTI system with the property that if the input...

We want to design a causal discrete-time LTI system with the property that if the input is

then the output is

(a) Determine the impulse response h (n) and the system function H (z) of a system that satisfies the foregoing conditions.

(b) Find the difference equation that characterizes this system.

(c) Determine a realization of the system that requires the minimum possible amount of memory.

(d) Determine if the system is stable.