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Fast Fourier transform

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A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. A FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from

Fast Fourier transform - Wikipedia Jump to content From Wikipedia, the free encyclopedia Discrete Fourier transform algorithm "FFT" redirects here. For other uses, see FFT (disambiguation) . An example FFT algorithm structure, using a decomposition into half-size FFTs A discrete Fourier analysis of a sum of cosine waves at 10, 20, 30, 40, and 50 Hz Time-based representation (above) and frequency-based representation (below) of the same signal, where the lower representation can be obtained from the upper one by Fourier transformation A fast Fourier transform ( FFT ) is an algorithm that comput

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