Official PYQ · 2023Set 1 · Q38LTI SystemsMCQ2 marks

GATE EC 2023 Set 1 Q38 — LTI Systems

Let an input $x[n]$ having discrete-time Fourier transform

$X\left(e^{j \Omega}\right)=1-e^{-j \Omega}+2 e^{-3 j \Omega}$ be passed through an LTI system. The frequency response of the LTI system is $H\left(e^{j \Omega}\right)=1-\frac{1}{2} e^{-j 2 \Omega}$ . The output $y[n]$ of the system is

Choose one optionA

\delta[n]+\delta[n-1]-\frac{1}{2} \delta[n-2]-\frac{5}{2} \delta[n-3]+\delta[n-5]

\delta[n]-\delta[n-1]-\frac{1}{2} \delta[n-2]-\frac{5}{2} \delta[n-3]+\delta[n-5]

\delta[n]-\delta[n-1]-\frac{1}{2} \delta[n-2]+\frac{5}{2} \delta[n-3]-\delta[n-5]

\delta[n]+\delta[n-1]+\frac{1}{2} \delta[n-2]+\frac{5}{2} \delta[n-3]+\delta[n-5]

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Answer: C

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Published 10 Oct 2026

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