A causal system H(z) is excited by x(n) and produces an output y(n). H(z) is described by (15pts) x(n) -1/4 a. Give a single difference equation in terms of 1=0 M y(n) = {b,x(n-1)- a_y(nm). -1/4 m=1 (define a's and b's precisely in terms of numerical values) b. Derive the impulse response of the system in closed form. y(n) c. Give the steady state response to the input x(n)=3u(n) - cos(rn/2-/4)