5.2 Periodicity and Periodic Extension

Definition 5.2.1 (Periodic function). A function \(f(x)\) is said to be periodic with period \(T\) if \(f(x + T) = f(x)\) for all \(x\).

The smallest positive \(T\) is said to be the fundamental period. If a function \(f(x)\) is not periodic, it can extended periodically, with period \(2\pi \), since the trigonometric functions are periodic with period \(2\pi \).