GATE 2015 EC – Question 61

Communications · Analog Communications · 2 marks · Numerical answer

In the system shown in Figure (a), $m(t)$ is a low-pass signal with bandwidth $W$ Hz. The frequency response of the band-pass filter $H(f)$ is shown in Figure (b). If it is desired that the output signal $z(t) = 10x(t)$, the maximum value of $W$ (in Hz) should be strictly less than ________.

(a) $x(t) = m(t)\cos(2400\pi t)$ goes through an amplifier giving $y(t) = 10x(t) + x^2(t)$, then through a band-pass filter $H(f)$ to give $z(t)$. (b) $H(f)$ equals 1 for $700 < |f| < 1700$ Hz and is 0 elsewhere.

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Correct answer: 349 to 350

Explanation

The carrier is at 1200 Hz, so $x(t)$ occupies $1200 \pm W$, which must lie inside the passband 700 to 1700 Hz, so $W < 500$. The term $x^2(t)$ has components near 0 up to $2W$ and near 2400 Hz from $2400 - 2W$ to $2400 + 2W$. These must fall outside the passband, so $2W < 700$ and $2400 - 2W > 1700$. Both give $W < 350$. So $W$ must be strictly less than 350 Hz.