Question

A \(4 \times 1\) multiplexer is used to multiplex 3 signals \(\{A, B, C\}\) with highest frequency components \(\{250 \text{ Hz}, 100 \text{ Hz}, 600 \text{ Hz}\}\) respectively. Each channel is uniformly sampled at a constant rate with the help of a channel selector clock (\(F_{\text{sel}}\)). The input channels \(\{I_1, I_2, I_3, I_4\}\) of the multiplexer are connected to the signals as \(\{A, C, B, C\}\) respectively. What is the minimum value for \(F_{\text{sel}}\) in order to recover the signals from their samples?

• A. 100 Hz
• B. 500 Hz
• C. 600 Hz
• D. 1200 Hz

Hint:

Remember the Nyquist-Shannon sampling theorem. The sampling rate should be at least twice the highest frequency component in the signal, otherwise, you will not be able to reconstruct it accurately.

Answer 1

The Correct Option is D

Step 1: According to the Nyquist-Shannon sampling theorem, the minimum sampling frequency (\(F_{\text{sample}}\)) should be at least twice the maximum frequency component of the signal to avoid aliasing and reconstruct the signal accurately. 
Step 2: The signals being multiplexed are \(\{A, C, B, C\}\) with frequencies \(\{250 \text{ Hz}, 600 \text{ Hz}, 100 \text{ Hz}, 600 \text{ Hz}\}\) respectively. The highest frequency component is 600 Hz. 
Step 3: Therefore, we need the sampling frequency as: \[ F_{\text{sample}} = 2 \times 600 = 1200 \text{ Hz} \] Since we are uniformly sampling each channel, the channel selector clock has to be at least 1200 Hz.