Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, computer science, and electrical engineering, the discrete Fourier transform (DFT), occasionally called the finite Fourier transform, is a transform for Fourier analysis of finite-domain discrete-time signals. As with most Fourier analysis, it expresses an input function in terms of a sum of sinusoidal components by determining the amplitude and phase of each component. Unlike the Fourier transform, which operates upon continuous functions assumed to extend to infinity, the DFT operates upon discrete and finite sets of values: the input to the DFT is a finite sequence of real or complex numbers, which makes the DFT ideal for processing information stored in computers. In particular, the DFT is widely employed in signal processing and related fields to analyze the frequencies contained in a sampled signal, to solve partial differential equations, and to perform other operations such as convolutions.

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