Question: Inputs to an ideal low-pass filter with frequency response leil0w H(e) = 3

Inputs to an ideal low-pass filter with frequency response

leil0w H(e

are given below. Find the corresponding outputs yi[n] i = 1, 2, 3.

(a) x1 [n] = 1+cos(0.3Ï€n) + 23 sin(0.7Ï€n), ˆ’ ˆž < n < ˆž .

(b) x2 [n] = δ[n] + 2δ[n ˆ’ 4].

(c) x3 [n] has DTFT X(ejω) = H(ejω/2).

leil0w H(e") = 3<ω< else in-π < ω π HΙα

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