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 convolution can be performed very efficiently using fast Fourier transforms.
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.
The embedded DSP mathblocks feature 18 bit x 18 bit multiply-accumulate blocks enabling efficient implementation of DSP building blocks, such as finite impulse response (FIR) filters, infinite impulse response (IIR) filters, and fast Fourier transforms (FFT).
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.
Rokhlin, Fast Fourier transforms for nonequispaced data, SIAM J.
Dual channel 16K point Fast Fourier Transforms with the appropriate filtering;
AirNet brings over 10 years of broadband, software-defined radio product expertise utilizing orthogonal frequency division multiplexing ("OFDM") technology implementing Fast Fourier Transforms ("FFT") to the WiMAX Forum.
The library, initially available with a FORTRAN interface, is comprised of a full implementation of optimized Level 1, 2 and 3 Basic Linear Algebra Subroutines (BLAS), Linear Algebra Package (LAPACK) as well as Fast Fourier Transforms (FFTs) in single-, double-, single-complex and double-complex data types.
0 is a collection of reusable linear algebra, Fast Fourier Transforms and vector math and statistical functions with a common applications programming interface.
The library, to be made available with both FORTRAN and C interfaces, will be comprised of a full implementation of Level 1, 2 and 3 Basic Linear Algebra Subroutines (BLAS), Linear Algebra Package (LAPACK) as well as Fast Fourier Transforms (FFTs) in single-, double-, single-complex and double-complex data types.
The cluster edition of Intel MKL also includes ScaLAPACK and distributed memory Fast Fourier Transforms.

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