Question 2014.S3.34: A sinusoid x(t) of unknown frequency is sampled by an impuls......

Wiley Acing The Gate Electrical Engineering [1079382]

A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with a cut-off at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) has a frequency of

(a) 10 Hz (b) 60 Hz (c) 30 Hz (d) 90 Hz

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We have $f_{\mathrm{s}}=50$ Hz. Let the frequency of signal at x(t) be $f_{\mathrm{x}}$ . Then

Given that LPF = 25 Hz, output = 20 Hz.
Therefore, the lower component, that is $(f_{s}-f_{x})$ passes through the filter $50\,-\,f_{x}=20\Rightarrow f_{x}=30\,\mathrm{Hz}$

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