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?