# 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 analyses procedures involved two parts; the detection of the faulty insulation using Fast Fourier Transform (FFT) and pattern recognition using Wavelet Analysis (WA).
Analysis of power quality of coal mine grid based on all-phase Fast Fourier transform, Power System Protection and Control.
Three control methods were tested on an actual SAPF model: the Butterworth filter method with successive 4th-order transformation, Fast Fourier transform method and the newly developed comparative method.
Gaussian and Fast Fourier Transform is implemented in this research.
However, as before, efficient implementation is possible using fast Fourier transforms.
The effectiveness of the Continuous Wavelet Transform (CWT) applied to transient signals in the computation of on-line Frequency Response Analysis curves for transformers has been evidenced in this study, showing that on-line IFRA based on CWT outperformed the correspondent one based on Fast Fourier Transform (FFT) in terms of repeatability, smoothness and signal de noising.
Therefore the comparison of the 2D spectrum pictures shows that the Short Fast Fourier Transform is the most expedient tool to obtain the attenuation time because the attenuation line is well visible (Figure 2) while the wavelet transform is more appropriate to detect the resonant frequencies in the suspension dynamics due to the better frequency resolution (Figure 5) and the possibility to analyze abrupt changes in signal.
Application of the Fast Fourier Transform yields information concerning the power of the oscillation as a function of the period.
BLAS Basic Linear Algebra Subprograms * FIT Fast Fourier Transform * GPGPU General-purpose Computing on Graphics Processing Units * GPU Graphics Processing Unit * KNC Knights Corner * MIC Many Integrated Core * MIMD Multiple Instruction Multiple Data * MPI Message Passing Interface * SIMD Single Instruction, Multiple Data * SIMT Single Instruction Multiple Thread * SM Streaming Multiprocessor * SMP Symmetric Multiprocessing * SSE Streaming SIMD Extensions * TACC Texas Advanced Computer Center
Lee, "Accelerating the nonuniform fast Fourier transform," SIAM Review, Vol.
The properties of the DHT are similar to those of the discrete Fourier transform (DFT) and Fast Hartley transform (FHT)  which is similar to the familiar Fast Fourier Transform (FFT).
Holograms are generated from these images by Fast Fourier Transform (FFT), adding in red, green and blue planes.

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