High Quality Content by WIKIPEDIA articles! The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum. For instance, the transform of a musical chord made up of pure notes is a mathematical representation of the amplitudes (and phase) of the individual notes that make it up. The composite waveform depends on time, and therefore is called the time domain representation. The frequency spectrum is a function of frequency and is called the frequency domain representation. Each value of the function is a complex number (called complex amplitude) that encodes both a magnitude and phase component. The term "Fourier transform" refers to both the transform operation and to the complex-valued function it produces.