A real signal x(t) is band-limited to f W/2. It passes through an LTI system with H(f)=e-j4 f for f W/2 and zero otherwise. Find the output.

GATE 2014 EC (EC4) – Question 28

Networks, Signals and Systems · LTI Systems · 1 mark · Multiple choice

A real signal x(t) is band-limited to $|f|\le W/2$. It passes through an LTI system with $H(f)=e^{-j4\pi f}$ for $|f|\le W/2$ and zero otherwise. Find the output.

$x(t+4)$
$x(t-4)$
$x(t+2)$
$x(t-2)$

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Correct answer: (D) $x(t-2)$

Explanation

Within the entire support of X(f), H(f)=exp(−j4πf)=exp(−j2πf×2), the frequency response of a delay of2time units. Outside that band X(f)=0, so the cutoff removes no input content. The output is therefore **x(t−2),D**.