The spectrum of a band pass signal spans from 20 kHz to 30 kHz. The signal can be recovered ideally from the sampled values when the sampling rate is at least:

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This question was previously asked in

ESE Electronics 2010 Paper 2: Official Paper

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Answer 1

Concept:

Sampling frequency of bandpass signal is given by:

\({f_S} \ge \frac{{2{f_H}}}{k}\)

Where

\(k = \left[ {\frac{{{f_H}}}{{{f_H} - {f_L}}}} \right]\) (Where [ .] denotes the floor value)

Analysis:

fH = 30 kHz

fL = 20 kHz

fH - fL = 10 kHz

\(k = \left[ {\frac{{30}}{10}} \right] = 3\) (floor value is 3)

\({f_S} \ge \frac{{2{f_H}}}{k} \ge 2\frac{{30}}{3} \ge 20~ kHz\)

so minimum sampling frequency is 20 kHz