1.

Consider two real valued signals, x(t) band-limited to [−500Hz, 500Hz] and y (t) bandlimited to [−1kHz, 1kHz]. For z(t) = x(t) . y(t), the Nyquist sampling frequency (in kHz) is __________ 

Answer»

x(t) is band limited to [−500Hz, 500Hz] 

y (t) is band limited to [1000Hz, 1000Hz]

z(t) = x (t) .y(t)

Multiplication in time domain results convolution in frequency domain.

The range of convolution in frequency domain is [−1500Hz, 1500Hz] 

So maximum frequency present in z(t) is 1500Hz Nyquist rate is 3000Hz or 3 kHz 



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