# 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.

## 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].
References in periodicals archive ?
The spectral analysis through Fourier transform obtained an extensive use, especially when switching to discrete and fast Fourier transforms.
The convolution can be performed very efficiently using fast Fourier transforms.
Nguyen, "An accurate algorithm for nonuniform fast Fourier transforms (NUFFT)," IEEE Microwave and Guided Letters, Vol.
The volume is divided into nine sections covering dense linear algebra, sparse linear algebra, multi-grid methods, fast Fourier transforms, combinational algorithms, stencil algorithms, bioinformatics, molecule modeling and advanced topics.
EEG was recorded at 17 electrode positions and fast Fourier transforms (FFT) determined power at Theta, Alpha-1, Alpha-2, Beta-1 and Beta-2.
Their topics include static variation compensators, harmonics, computational tools and programs for designing and analyzing compensators and filters, monitoring power quality, capacitors, and fast Fourier transforms.
These applications include zoom fast Fourier transforms (FFTs), octave analyses, short-time Fourier transforms, order analyses, and more time and frequency tools.
Rokhlin, Fast Fourier transforms for nonequispaced data, SIAM J.
We use a fast summation algorithm based on Nonequispaced Fast Fourier Transforms, building on previous work that used Fast Multipole Methods.
Using fast Fourier transforms, the PIMM can determine the frequency dependence of the complex magnetic permeability as well as the step and impulse responses of magnetic systems.
EFFECT OF PHASE ON FAST FOURIER TRANSFORMS WITH APPLICATIONS TO TIME-SERIES PHOTOMETRY Travis Laurance * and Eric Klumpe, Middle Tennessee State University, Murfreesboro, Tennessee.
Simulation waveform analysis with MicroSim Probe (included in both packages) delivers significantly more analysis information than other packages and includes multiple plot windows, fast Fourier transforms and analysis of more complex functions.

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