Periodic Extension

Definition 5: Periodic Extension

The periodic extension of a function $f$ defined on $[a,b]$ is the $b-a$ periodic function $f_p$ such that

• $f_p(t)=f(t)$ for $t\in (a,b)$ where $f(t)$ is continuous.
• $f_p(t)=\frac{f(t^{-})+f(t^{+})}{2}$ for $t\in (a,b)$ where $f(t)$ is not continuous.
• $f_p(a)=\frac{f(a)+f(b)}{2}=fp(b)$