Fourier analysis, based off of the Fourier series, is a breakdown of a function in terms of a sum of its basis functions. In other words, in Fourier analysis, a complicated equation can be broken down into several simpler equations. On its discovery, Fourier analysis allowed the solving of many previously unsolvable mathematical problems. e-dsp.com: What are Fourier Series?

A function is a mathematical equation that manipulates a number. Not all equations are functions. For an equation to be a function, each input into the function must have a discrete output. If two inputs into the function give the same output, then the equation is not a function. Functions can be represented as equations or graphically. Purple math: Functions versus relations

• Oregon State University: FFT History