EC > GATE 2023 > LTI Systems
Let an input x[n] having discrete time Fourier transform
X(ejΩ) = 1 - e-jΩ + 2e-3jΩ be passed through an LTI system. The frequency response of the LTI system is H(ejΩ) = 1 - 1/2 e-j2Ω. The output y[n] of the system is
A
δ[n] + δ[n - 1] - 1/2 δ[n - 2] - 5/2 δ[n - 3] + δ[n - 5]
B
δ[n] - δ[n - 1] - 1/2 δ[n - 2] - 5/2 δ[n - 3] + δ[n - 5]
C
δ[n] - δ[n - 1] - 1/2 δ[n - 2] + 5/2 δ[n - 3] - δ[n - 5]
D
δ[n] + δ[n - 1] + 1/2 δ[n - 2] + 5/2 δ[n - 3] + δ[n - 5]

Correct : b

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frequency response LTI system discrete time Fourier transform GATE EC 2023 LTI system output convolution theorem EC gate system frequency response discrete time signals

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