Consider an LTI system with impulse response h(n) = [(1/4)u cos(/4n)] (a) Determine its system function H(z)

Question:

Consider an LTI system with impulse response h(n) = [(1/4)u cos(π/4n)]
(a) Determine its system function H(z)
(b) Is it possible to implement this system using a finite number of adders, multipliers and unit delays? If yes, how?
(c) Provide a rough sketch of |H(ω)| using the pole-zero plot.
(d) Determine the response of the system to the input x(n) = (1/4)nu (n)