How to Determine Whether a Signal is Periodic or Not

When  a signals repeats an exact pattern after a fixed time period, it’s considered as a periodic signal. And this will continue to repeat for an infinite amount of time. The fixed time that takes to complete the repeated unit shape is known as the fundamental period T0.

A continues time CT signal is a signal that has values for every instant of time. On the other hand, a discrete signal DT has only values for predefined set of integers. The both the continues time signal and the discrete time signals can have periodic and non periodic signals.

Concept

In order to be a periodic signal, it need to be repeated after a fixed time period which is known as a period T. So if the function of a periodic signal is x(t), it should be the same signal after changing the time period by period T0.

Lets consider the graphs

by substituting integer values for n.

As you can see, we get the same graph for all the integer values of n.

The Periodic Signal

Every periodic signal must satisfy,

So, in order to be a periodic signal, the function of the signal must satisfy the following condition.

T0 is the fundamental period of the signal which is the minimum positive period of interval. The corresponding frequency and the angular frequency to the fundamental period is known as the fundamental frequency (f0) and the fundamental angular frequency (ω0).

Fundamental frequency (f0)

Fundamental angular frequency (ω0)