Definition:Periodic Real Function/Frequency

Definition

Let $f: \R \to \R$ be a periodic real function.

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

$\nu = \dfrac 1 L$

where:

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

Also denoted as

In some contexts, the frequency of a periodic real 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.

Also see

• Definition:Angular Frequency

• Results about the frequency of a periodic real function can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): frequency: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): frequency: 1.