A complex low pass signal has a bandwidth of 100khz. What is the minimum sampling rate for this signal
Answers
Normally, the complex low-pass signal has the bandwidth of 200 kHz and its bandwidth of low-pass signal is between 0 and f.
In the solution, f is the maximum frequency where signal and f is the maximum frequency in the signal.
Signal with L levels can carry log2L bits per level.
According to the Nyquist-Shannon sampling theorem, for a signal with a bandwidth b, the minimum sampling rate needed to accurately sample the signal is 2b or twice the bandwidth. This of course assumes that the signal is band-limited which means that there are no frequencies higher than b in the signal. The problem conveniently mentions that the signal is a "low pass" signal, which satisfies this condition.
Thus, for this signal with bandwidth = 100 kHz, the minimum sampling rate would be 200 kHz.
Note that in practice, a sampling rate slightly above 200 kHz will be used to sample such a signal to account for the signal phase. However, this is probably beyond what the problem asks for. This is only to inform you of the difference between the theory and practice.