Let x 1(t) and x 2(t) be two band-limited signals having bandwidth B=4103 rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is

GATE 2023 EC – Question 50

Communications · Analog Communications · 2 marks · Multiple choice

Let $x_1(t)$ and $x_2(t)$ be two band-limited signals having bandwidth $B=4\pi\times10^3$ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample $y(t)$, is

$20\pi\times10^3$
$40\pi\times10^3$
$8\pi\times10^3$
$32\pi\times10^3$

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Correct answer: (D) $32\pi\times10^3$

Explanation

$x_1$ is multiplied by $\cos(4\pi\times10^3t)$, so it occupies up to $4\pi\times10^3+4\pi\times10^3=8\pi\times10^3$ rad/s. $x_2$ is multiplied by $\cos(12\pi\times10^3t)$ and occupies up to $12\pi\times10^3+4\pi\times10^3=16\pi\times10^3$ rad/s. The highest frequency in $y(t)$ is $16\pi\times10^3$, so the Nyquist rate is $2\times16\pi\times10^3=32\pi\times10^3$ rad/s.