is a linear operator that maps functions to other functions. The Fourier transform decomposes a function into a continuous spectrum of its frequency components, and the inverse transform synthesizes a function from its spectrum of frequency components. A useful analogy is the relationship between a series of pure notes (the frequency components) and a musical chord (the function itself). In mathematical physics, the Fourier transform of a signal can be thought of as that signal in the "frequency domain." This is similar to the basic idea of the various other Fourier transforms including the Fourier series of a periodic function.