# 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 averaging values reflect the change of wind speed over time of the year and the seasonality of wind environment in the two cities are further investigated in detail by conducting Fast Fourier Transform (FFT) of the one-year wind data and results are shown in Figure 1.
Aggarwal, "Digital image Watermarking using Two Dimensional Discrete Wavelet Transform, Discrete Cosine Transform and Fast Fourier Transform," International Journal of Recent Trends in Engineering, vol.
Zeng, "Measuring residual stress of anisotropic thin film by fast Fourier transform," Optics Express, vol.
The processing procedure are divided into two stages; Fast Fourier Transform (FFT) and Wavelet Analysis (WA).
Finally, all the results via the reduction technique based on complex modes (for the time series, the spectral content, and the limit cycles with the Fast Fourier Transform) are in perfect agreement with the reference performed via the finite element model without any interface condensation.
We combined the matrix form of this discrete Laplace transform with a generalized fast Fourier transform in a purely algebraic fashion, where we used the decomposition of the Laplace transform explicitly and a small number of generalized FFTs as black box.
To design such antenna patterns we adopted an iterative fast Fourier transform method [13, 14].
In this paper, we propose a new fast Fourier transform subspace-based optimization method (NFFT-SOM) which avoids a full SVD of [[??].sub.[partial derivative]], and fast Fourier transform can be used to accelerate the computational speed at the same time.
The purpose of this research is segmentation of optic disc using the combination of Gaussian dan Fast Fourier Transform and median filter as the preprocessing stage and binary thresholding for the detection of the optic disc in the retinal image.
The derived (D), the discrete fast Fourier transform (DFFT), the discrete cosine transform (DCT), and the discrete wavelet transform (DWT).
What this means is a Fast Fourier Transform can decompose A-scans to yield a separate acoustic image for each sinusoid.

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