Periodic function

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Example of a periodic function, with period ${\displaystyle T}$. If you choose any point on the function and then move to the left or right by ${\displaystyle T}$, you will find the same value as at the original point.

In mathematics a periodic function is a function that repeats itself after a while, and indefinitely. The mathematical definition of this is that ${\displaystyle f(t)}$ is periodic with period ${\displaystyle T}$ if

${\displaystyle f(t+T)=f(t)\ \ \forall \ t\in \mathbb {R} \ .}$

Common examples of periodic functions are ${\displaystyle \sin(\omega t)}$ and ${\displaystyle \cos(\omega t)}$, which both have period ${\displaystyle 2\pi /\omega }$.

A sawtooth wave is a periodic function that can be described by

${\displaystyle f(x)={\begin{cases}|x-1|&{\text{if }}-1<x<1,\\f(x+2)&{\text{if }}x\leq -1,\\f(x-2)&{\text{if }}x\geq 1.\end{cases}}}$