4.24 Suppose we are given a stationary zero-mean series xt with spectrum fx() and then construct the

4.24 Suppose we are given a stationary zero-mean series xt with spectrum fx(ω) and then construct the derived series yt = ayt−1 + xt, t= ±1,±2, ... .

(a) Show how the theoretical fy(ω) is related to fx(ω).

(b) Plot the function that multiplies fx(ω) in part

(a) for a = .1 and for a = .8. This filter is called a recursive filter.