📂Functions

Quasiperiodic function

Definition ¹

A function $h : \mathbb{R} \to \mathbb{R}^{n}$ is said to be quasiperiodic if it can be expressed in terms of a basic frequency $\omega_{1} , \cdots , \omega_{n}$ and for each $x_{1} , \cdots , x_{n}$ there exists a $2 \pi$-periodic function $H$ such that the following holds $h$. $$h(t) = H \left( \omega_{1} t , \cdots , \omega_{n} t \right)$$

Explanation

A quasiperiodic function is not literally a periodic function, but it possesses similar properties. For instance, the $h$ defined as follows is a quasiperiodic function. $$h(t) = r_{1} \cos \omega_{1} t + r_{2} \sin \omega_{2} t$$

On the other hand, a quasiperiodic function with infinitely many basic frequencies may also be referred to as an almost periodic function.