Period measurement is an input signal parameter. So, the controller you are using will have an Enhanced capture timer (ECT) for input capture of a signal. Here you can initialise this timer for capturing the signal on either rising edges or falling edges. The difference between one ising edge and the next rising edge will give you the period. But this timer has a timer interrupt and an overflow interrupt. You can capture the signal on interrupt basis and handle the overflow for long events. I suggest you read the datasheet of the controller.
Good luck.
