Let xt = cos(2t), and consider the output yt = X k= akxtk, where P k |ak| < . Show yt = |A()| cos(2t +

Let xt = cos(2πωt), and consider the output yt = X∞

k=−∞

akxt−k, where P k |ak| < ∞. Show yt = |A(ω)| cos(2πωt + φ(ω)), where |A(ω)| and φ(ω) are the amplitude and phase of the filter, respectively.

Interpret the result in terms of the relationship between the input series, xt, and the output series, yt.