# How to Calculate the Period of the Discrete Time Sequence from Taking Its DFT

This is my discrete time periodic signal, the time resolution of the samples is 0.2ms.

And it's periodic after each 11 samples. So the fundamental period of the signal is 2ms or the fundamental frequency of this sequence is 500Hz. The amplitude of each pulse increases from -5V with unit step to +5V.

But I want to find its frequency (which is 500 Hz) by calculating its FFT and plot of FFT spectrum. Please help me. Thank you.

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.

• The peak frequency in the spectrum is not always the period. – hotpaw2 Jun 26 '15 at 4:18
• @hotpaw2, I didn't implied so. In this case it will. By the way, if the signal is noise free this rule of thumb would quite good. – Royi Jun 26 '15 at 8:44
• @hotpaw2 Peak frequency in the spectrum is not always the period: not even for a sinusoid? can you give example? – Creator Jul 13 '15 at 20:29
• A sinusoid plus another sinusoid related by a fraction composed of 2 relative primes. The signal created by the sum has a different period than either component sinusoid. – hotpaw2 Jul 14 '15 at 0:05
• Sir I am giving a periodically repeating data here in the form of a row vector. Please make the calculations and clear it. data = [1.5 4 -0.5 1.25 1.75 0.25 3.1 2.30 1.5 4 -0.5 1.25 1.75 0.25 3.1 2.30 1.5 4 -0.5 1.25 1.75 0.25 3.1 2.30 1.5 4 -0.5 1.25 1.75 0.25 3.1 2.30]. Use this matrix to do calculations.. – JOSHY T R Aug 19 '15 at 11:42