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The Nyquist sampling rate for the signal x(t) = (sin(500πt))/(πt) × (sin(700πt))/(πt) is given by

1. 400 Hz
2. 600 Hz
3. 1200 Hz
4. 1400 Hz

Correct answer: 1200 Hz

Solution

sin(500 pi t)/(pi t) has bandwidth 250 Hz and sin(700 pi t)/(pi t) has 350 Hz. Their product convolves the spectra, giving total bandwidth 600 Hz, so the Nyquist rate is 2*600=1200 Hz, not 1400 Hz.

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