GATE 2014 EC (EC2) – Question 62
The figure gives the message spectrum M(f), with A = 100 Hz and B = 40 Hz. Modulating signals are $v(t)=\cos(2\pi f_ct)$ and $w(t)=\cos(2\pi(f_c+A)t)$, with $f_c>A$. Both filters have cutoff $f_c$. Find output signal bandwidth (Hz).
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Correct answer: 59.9 to 60.1
Explanation
The first mixer shifts the message bands to±fc. The high-pass filter with cutofffc retains the positive upper sideband fc+B through fc+A and its negative-frequency mirror. Mixing with fc+A translates these to baseband intervals−(A−B)through0and0through A−B. The low-pass output therefore has bandwidth **A−B=60Hz**.