# Definition:Periodic Function/Frequency

## Definition

Let $f: X \to X$ be a periodic function, where $X$ is either $\R$ or $\C$.

The frequency $\nu$ of $f$ is the reciprocal of the period $L$ of $f$:

$\nu = \dfrac 1 L$

where:

$\forall x \in X: \map f x = \map f {x + L}$

where $\size L$ is the modulus of $L$.

## Also defined as

In some contexts, the frequency of a periodic function is given by the letter $f$, but as this letter is also used for the general function, this can be seen often to be inadequate.