Fourier analysis

The decomposition of a wave form into more elemental wave forms which when summed approximately reproduce the original wave. Decomposition of this sort is often done because it is simpler to operate on the components of a complex wave than the wave itself. Wolfram says: “A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series is known as harmonic analysis and is extremely useful as a way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical.”