Question: Consider the problem of approximating the filter output yt = X k= akxtk, X |ak| < , by yM t = X |k|

Consider the problem of approximating the filter output yt = X∞

k=−∞

akxt−k, X∞

−∞

|ak| < ∞, by yM t = X

|k|

X−1 k=0 A(ωk) exp{2πiωkt}

with ωk = k/M. Prove E{(yt − yM t )

2} ≤ 4γx(0) X

|k|≥M/2

|ak|

2

.

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