Generalized Fourier series

Generalized Fourier series is like a puzzle. Imagine someone cutting a picture of a favorite animal into many small pieces, then mixing them up so they don't all make sense together. Generalized Fourier series takes these small pieces and rearranges them so they fit together again. It takes the original information (like the animal picture) and breaks it down into simpler parts, which can then be joined back together in different ways to create something new.