Periodic function

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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

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

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

${\displaystyle f(x)=\{\begin{array}{ll}|x-1|& \text{if }-1<x<1,\\ f(x+2)& \text{if }x\le -1,\\ f(x-2)& \text{if }x\ge 1.\end{array}}$