How to Calculate the Period of the Discrete Time Sequence from Taking Its DFT
Sample the signal into MATLAB.
Apply the fft function on it.

Plot the absolute value of the DFT signal (Its first half of samples).
Look for its peak, the index number of the peak multiplied by the sampling frequency divided by the number of samples will give the frequency.
Look at its inverse and your answer will pop.

If you upload a digital copy of the signal, I will show you in code.