Decomposition

Writing a complicated periodic function as a sum of a few simple periodic pieces.

Informally, decomposition means writing a complicated periodic function as a sum of simple periodic pieces, each fully described by three numbers -- amplitude (how big it is), frequency (how fast it repeats), and phase (where in its cycle it starts). Fourier's claim, made rigorous starting in Chapter 2, is that sines and cosines are always enough pieces to do this with.

Examples

A square wave decomposes into infinitely many odd harmonics of a fundamental sine wave, each with its own amplitude.