# Is the unit step function periodic?

I am confused regarding the unit step signal. Is it considered to be periodic signal or non-periodic signal?

In MATLAB we use command heaviside to implement it but then that graph always shows a horizontal straight line after time is greater than equal to zero.

I am very confused. If it is periodic, what is its period?

• no
– Jdip
Mar 16, 2023 at 6:08

If the signal is considered over the interval (-$$\infty$$, $$\infty$$) the signal is not periodic as for any value of T (time-period) the signal does not repeat itself.

Now if one starts looking at a portion of the signal in the (-$$\infty$$, 0) or [0, -$$\infty$$), the question of signal being periodic comes into picture. However, the time-period (after which the signal repeats it-self) is infinitesimally small and the frequency of the signal is not finite. Hence for all practical applications unit step is not considered periodic.

• Note that a constant signal, such as $f(t) = 1$, is periodic. It doesn't have a fundamental period, though.
– MBaz
Mar 16, 2023 at 13:38

A continuous time Unit step function is not periodic in time. A function f(t) will be periodic if it satisfies the condition: f(t+T) = f(t), for all t, where T is a non-zero positive real number. This means the function f(t) repeats itself after every t = T. The term T is called the fundamental time period of f(t).

In a different approach, we can say that the unit step function is periodic with a time period T equal to infinity. This means that the step function repeats itself only at infinity.

• I don't think there's any justification to say that a time period can be equal to infinity. Infinite is not a number.
– MBaz
Mar 16, 2023 at 13:39
• No, this is just an approach or a mathematical way of saying that the signal is not periodic. T is infinite means the signal repeats at infinity, which logically means the signal doesn't repeat itself Mar 19, 2023 at 0:53