Question: what is the periodic extension?
Answer: There are two periodic extensions for f(x) that are very useful. Given any f(x), which is. defined only for 0 <x<ℓ, we define its even periodic extension, Fe(x), by the conditions that a) Fe(x) = f(x) for 0 <x<ℓ b) Fe(x) is even (This fixes Fe(x) for −ℓ<x< 0.)