Pulse Train Sampling Rate
You need to describe your "pulse train" in greater detail, but in general, your sample interval (period) needs to be strictly shorter than the shortest "high" or shortest "low" that can appear in your signal. Otherwise, you risk missing a high or a low altogether.

UARTs use high sample rates in order to deal with "sloppy" signals that might have significant noise or distortion. It also makes them more tolerant of speed errors between the two ends of the connection.