We want to design a causal discrete-time LTI system with the property that if the input is
x(n) = (1/2)nu(n) – ¼(1/2) n – 1 u(n – 1)
then the output is
y(n) = (1/3)nu(n)
(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.