GATE 2014 EC (EC1) – Question 28
Real signals x(t) and y(t) are band-limited to [−500,500] Hz and [−1,1] kHz, respectively. For z(t) = x(t)y(t), find the Nyquist sampling frequency (kHz).
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Correct answer: 2.99 to 3.01
Explanation
Multiplication in time convolves the two spectra. Their support intervals add:±500Hz and±1000Hz produce a possible support extending to±1500Hz. Twice the highest frequency is3000Hz, so the Nyquist sampling frequency is **3kHz**. It is the sum of bandwidth limits, not their larger value.