Fast Fourier Transform
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fast Fourier transform
[¦fast ‚fu̇r·ē‚ā ′tranz‚fȯrm] (mathematics)
A Fourier transform employing the Cooley-Tukey algorithm to reduce the number of operations. Abbreviated FFT.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
Fast Fourier Transform
(algorithm)(FFT) An algorithm for computing the Fourier transform of a set of discrete data values. Given a finite
set of data points, for example a periodic sampling taken from
a real-world signal, the FFT expresses the data in terms of
its component frequencies. It also solves the essentially
identical inverse problem of reconstructing a signal from the
frequency data.
The FFT is a mainstay of numerical analysis. Gilbert Strang described it as "the most important algorithm of our generation". The FFT also provides the asymptotically fastest known algorithm for multiplying two polynomials.
Versions of the algorithm (in C and Fortran) can be found on-line from the GAMS server here.
["Numerical Methods and Analysis", Buchanan and Turner].
The FFT is a mainstay of numerical analysis. Gilbert Strang described it as "the most important algorithm of our generation". The FFT also provides the asymptotically fastest known algorithm for multiplying two polynomials.
Versions of the algorithm (in C and Fortran) can be found on-line from the GAMS server here.
["Numerical Methods and Analysis", Buchanan and Turner].
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
FFT
(Fast Fourier Transform) A computer algorithm used in digital signal processing (DSP) to modify, filter and decode digital audio, video and images. FFTs commonly change the time domain into the frequency domain.Myriad Recognition Uses
FFTs are widely used in voice recognition and myriad other pattern recognition applications. For example, noise-cancelling headphones use FFT to turn unwanted sounds into simple waves so that inverse signals can be generated to cancel them. FFTs are used to sharpen edges and create effects in static images and are widely used to turn a number series into sine waves and graphs.
Fast DFT Processing
The FFT quickly performs a discrete Fourier transform (DFT), which is the practical application of Fourier transforms. Developed by Jean Baptiste Joseph Fourier in the early 19th century, the Fourier equations were invented to transform one complex function into another. One of Fourier's primary goals was to predict the rate of heat transfer based on temperature, mass and proximity. In practice, the terms FFT, DFT and Fourier transform are used synonymously. See DSP.
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| An FFT Transform |
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| A Fourier transform was used to chart the power levels at different frequencies from the half second of digital samples (top). |
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