A signal x(t) has a bandwidth 2B about a carrier frequency of f_{c} = 2 GHz as shown in Figure (a) below. In order to demodulate this signal, it is first mixed (multiplied) with a local oscillator of frequency f_{LO} = 1.5 GHz, and then passed through an ideal low-pass filter (LPF) with a cut-off frequency of 2.8 GHz. The output of the LPF is sent to a digitizer ADC with a sampling rate of 1.6 GHz as shown in Figure (b) below. The maximum value of B so that the signal x(t) can be reconstructed from its samples according to the Nyquist sampling theorem is ______ MHz.

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GATE IN 2019 Official Paper

CT 1: Ratio and Proportion

2846

10 Questions
16 Marks
30 Mins

The maximum value of B will be obtained in case of bandpass sampling

output of LPF

According to bandpass sampling

\({f_s} \ge \frac{{2fH}}{K}\)

\(1.6\;GHZ \ge \frac{{2\left( {0.5 + B} \right)}}{K}\)

\(1.6 \ge \frac{{2\left( {0.5 + B} \right)}}{{\left[ {\frac{{{f_H}}}{B}} \right]}}\)

\(\frac{{{f_H}}}{B} = \frac{{0.5 + B}}{{2B}}\)

\(1.6 \ge = \frac{{2\left( {0.5 + B} \right)}}{{\frac{{0.5 + B}}{{2B}}}}\)

1.6 ≥ 4B

B ≤ 0.4 GHZ

B ≤ 400 MHZ

So maximum value of B is 400 MHZ