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Topic: Fast Fourier transform

Related Topics

Discrete Fourier transform

FFT multiplication

Fourier transform

List of algorithms

Continuous Fourier transform

Convolution theorem

Circulant matrix

Frequency domain

Numerical stability

Deconvolution

Floating point

Digital signal processing

Stationary process

Fourier series

	fast Fourier Transform
		The transform of an infinite train of delta functions spaced by T is an infinite train of delta functions spaced by 1/T. The transform of a cos function is a positive delta at the appropriate positive and negative frequency.
		The transform of a sin function is a negative complex delta function at the appropriate positive frequency and a negative complex delta at the appropriate negative frequency.
		For example the transform of a truncated sin function are two delta functions convolved with a sinc function, a truncated sin function is a sin function multiplied by a square pulse.
	local.wasp.uwa.edu.au /~pbourke/other/dft (1664 words)

	Fast Fourier transform: Facts and details from Encyclopedia Topic (Site not responding. Last check: )
		Bruuns algorithm is a fast fourier transform (fft) algorithm based on an unusual recursive polynomial-factorization approach, proposed for powers of two by g....
		Raders algorithm (1968) is a fast fourier transform (fft) algorithm that computes the discrete fourier transform (dft) of prime sizes by re-expressing the...
		A discrete hartley transform (dht) is a fourier-related transform of discrete, periodic data similar to the discrete fourier transform (dft), with analogous applications...
	www.absoluteastronomy.com /encyclopedia/f/fa/fast_fourier_transform.htm (2918 words)

	Fast Fourier Transform : FFT (Site not responding. Last check: )
		FFTs became popular after J. Cooley of IBM and J. Tukey of Princeton published a paper in 1965 reinventing the algorithm and describing how to perform it conveniently on a computer (including how to arrange for the output to be produced in the natural ordering).
		FFT algorithm">Rader's algorithm, exploiting the existence of a generator for the multiplicative group modulo prime n, expresses a DFT of prime size n as a cyclic convolution of (composite) size n - 1, which can then be computed by a pair of ordinary FFTs via the convolution theorem (although Winograd uses other convolution methods).
		There are further FFT specializations for the cases of real data that have even/odd symmetry, in which case one can gain another factor of ~2 in time/space and the DFT becomes the discrete cosine/sine transform(s) (DCT/DST).
	www.termsdefined.net /ff/fft.html (2550 words)

	Fast Fourier Transform (FFT)
		Fourier transforms are also used to solve partial differential equations.
		For this example, the interval [0,6] is used instead of [—3,3] to input function [3] to the fast Fourier transform software.
		quadratic transformation For a VaR measure, a transformation procedure that is applicable to quadratic portfolios.
	www.riskglossary.com /articles/fast_fourier_transform.htm (978 words)

	ipedia.com: Cooley-Tukey FFT algorithm Article (Site not responding. Last check: )
		It re-expresses the discrete Fourier transform of an arbitrary composite size n = n 1 n 2 in terms of smaller DFTs of si...
		FFTs became popular after J. Cooley of IBM and John W. Tukey of Princeton published a paper in 1965 reinventing the algorithm and describing how to perform it conveniently on a computer (including how to arrange for the output to be produced in the natural ordering).
		See also the fast Fourier transform for information on other FFT algorithms, specializations for real and/or symmetric data, and accuracy in the face of finite floating-point precision.
	www.ipedia.com /cooley_tukey_fft_algorithm.html (2214 words)

	Fast Fourier Transform (FFT) - Origin
		The Fast Fourier Transform is used in linear systems analysis, antenna studies, optics, random process modeling, probability theory, quantum physics, and boundary-value problems (Brigham, 2-3) and has been very successfully applied to restoration of astronomical data (Brault and White).
		The mathematician Fourier recognized that a periodic function could be described as an infinite sum of periodic functions.
		Fast Fourier Transforms can be performed on Origin datasets by using the FFT Tool.
	www.originlab.com /index.aspx?s=8&lm=115&pid=75 (281 words)

	The FFT: Making Technology Fly
		Fourier analysis, in the guise of X-ray crystallography, was essential to Watson and Crick's discovery of the double helix, and it continues to be important for the study of protein and viral structures.
		Mathematically, the fast Fourier transform is based on a factorization of the Fourier matrix into a collection of sparse matrices--matrices in which most of the entries are equal to zero.
		The fast Fourier transform was seized upon by researchers interested in everything from signal detection in radar systems to the assessment of heart valve damage by biomedical instrumentation.
	www.siam.org /siamnews/mtc/mtc593.htm (1915 words)

	Using Sun Performance Library Fast Fourier Transform Routines
		Sun Performance Library FFT routines use the divide-and-conquer approach, where the transform of a sequence is a composite of transforms of shorter sequences.
		19, the transform of the vector corresponding to 4
		The Fourier transform of the vector [1 2 3 4] is:
	docs.sun.com /source/806-6147/FFT.html (3873 words)

	Fast Fourier Transform
		The fast Fourier transformation relies on the existence of a factorization of the input length N. Therefore assume N = mn for some integers m and n.
		For the transformation of 2 (d=0) or 4 (d=1) numbers there is a very nice alternative, since it is possible to avoid making any multiplications at all, thanks to the fact that all multiplications would anyway be by a power of the imaginary unit.
		JPS Also, for the FFT to really be considered fast, it almost necessarily would need to be written in C, e.g., as a TEA or with critcl or SWIG.
	wiki.tcl.tk /11244 (1889 words)

	FFT Links
		FFT Sources: This is the list of all the codes that we included in benchFFT, along with links to where they may be downloaded.
		Picture Book of Fourier Transforms by Kevin Cowtan gives an interesting graphical tutorial on the interpretation of 2D FFT output, with a special emphasis on crystallography.
		DFT Introduction by Paul Bourke, describing the discrete Fourier transform in terms of the continuous transform, with examples of the transforms of various functions.
	www.fftw.org /links.html (986 words)

	An application of Discrete Fast Fourier Transform algorithm
		In addition, the Fourier transform of the complex conjugate of a function f(x) is F(-s), the reflection of the conjugate of the transform*.
		Since the Fourier transform F(s) is a frequency domain representation of a function f(x), the s characterizes the frequency of the decomposed cosinusoids and sinusoids and is equal to the number of cycles per unit of x.
		You can use the FFT to determine the frequency of a note played in recorded music, to try to recognize different kinds of birds or insects, etc. The FFT is also useful for things which have nothing to do with audio, such as image processing (using a two-dimensional version of the FFT).
	www.bridgeport.edu /sed/projects/cs597/Summer_2002/kunhlee (2639 words)

	NERSC Fast Fourier Transform Software
		The Fast Fourier Transform (FFT) is the fast algorithm to compute the Discrete Fourier Transform.
		The Fourier transform subroutines in PESSL perform mixed-radix transforms in two and three dimensions.
		FFTs in IMSL are modeled on the Cooley-Tukey algorithm.
	www.nersc.gov /nusers/resources/software/libs/math/fft (511 words)

	SETTING UP THE FAST FOURIER TRANSFORM (Site not responding. Last check: )
		Unfortunately, the faster Fourier transform program is not so transparently clear as the programs given earlier.
		Flexibility may be lost because the basic fast program works with complex-valued signals, so we ordinarily convert our real signals to complex ones (by adding a zero imaginary part).
		In reality, the fast method is not quite that fast, depending on certain details of overhead and implementation.
	sepwww.stanford.edu /sep/prof/pvi/dft/paper_html/node14.html (649 words)

	FFTW Home Page
		FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e.
		The slides from the 7/28/98 talk "The Fastest Fourier Transform in the West," by M. Frigo, are also available, along with the slides from a shorter 1/14/98 talk on the same subject by S. Johnson.
		A preprint on a new FFT algorithm that, following James Van Buskirk, improves upon previous records for the arithmetic complexity of the DFT and related transforms, is: Steven G. Johnson and Matteo Frigo, "A modified split-radix FFT with fewer arithmetic operations", IEEE Trans.
	www.fftw.org (908 words)

	FFT Software - Fast Fourier Transform .NET Component, Visual Basic .Net, C++, C#
		To efficiently compute FFTs, it is important that the FFT algorithm is implemented efficiently in code to give maximum speed and reliability.
		When you are developing multiple applications or an application that needs to be maintained in the long term, within constraints of time and budget, probably the most effective use of your time is to pass the numerical processing to a tightly written, multithreaded component such as Transform/NET to handle it.
		The FFT algorithms are all written in highly efficient, 100 % managed Visual C# to ensure that you can achieve highly efficient, reliable spectral analysis within your applications or web site.
	windale.com /transformnet.php (855 words)

	FAST-FOURIER-TRANSFORM ( FTT ) DESCRIPTION (Site not responding. Last check: )
		It has been known for a long time that any waveform can be transformed into its frequency spectrum, or Fourier series, by a long mathematical process called the Fourier Transform, but it was too computationally intensive and computers were too slow for it to be of much use.
		The FFT transforms a waveform into a series of sines and cosines (or amplitudes and phase-angles) at each frequency present in the original signal.
		A FFT takes approximately (n/2) log2(n) complex multiplications to complete, or about 5000 for a 1024 point FFT Vs over (1 million for the original Fourier Transform; a 1024 point FFT will take about 0.1 second or less on a modern personal computer.
	www.vibrationworld.com /AppNotes\FFT.htm (436 words)

	Fast Fourier Transform
		Transforms were used to study sound waves, frequency vibrations, and other repetitive occurrences.
		Fourier analysis is the process of decomposing seemingly complex, chaotic data into a sum of sinusoids of different cycle lengths.
		Developed by Jean Baptiste Fourier in 1807, Fourier analysis proves that any given waveform can be broken down into a combination of sinewaves of different amplitude (maximum value), frequency (rate of vibration), and phase -- the three basic properties of cycles.
	www.traders.com /Documentation/FEEDbk_docs/Archive/072002/Abstracts_new/Wu/wu.html (320 words)

	Integer Fast Fourier Transform (INTFFT) - Oraintara, Chen, Nguyen (ResearchIndex)
		Abstract: In this paper, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced.
		Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has properties that it is an integer-to-integer mapping, power adaptable and also reversible.
		Split-radix FFT is used to illustrate the approach for the case of 2^N-point FFT.
	citeseer.ist.psu.edu /649349.html (411 words)

	Discrete Fourier Transform (Site not responding. Last check: )
		The transform of an infinite train of delta functions spaced by T is an infinite train of delta functions spaced by 1/T. The transform of a cos function is a positive delta at the appropriate positive and negative frequency.
		The transform of a sin function is a negative complex delta function at the appropriate positive frequency and a negative complex delta at the appropriate negative frequency.
		For example the transform of a truncated sin function are two delta functions convolved with a sinc function, a truncated sin function is a sin function multiplied by a square pulse.
	astronomy.swin.edu.au /~pbourke/analysis/dft (1075 words)

	FAQ: Discrete fast Fourier transform (Site not responding. Last check: )
		For many of us, the last time we saw a Fourier series was in math class, where the goal was to decompose a function on [0,2π] into its frequency components by expressing it as a linear combination of {sin(nx), cos(nx), n=0...
		Fortunately, the fast Fourier transform is an algorithm for computing the coefficients that is, well, very fast (Monahan 2001, section 14.5).
		You should to be aware that the FFT algorithm requires the number of sampled points to be a power of 2.
	www.stata.com /support/faqs/mata/fourier.html (1019 words)

	Deriving the Fast Fourier Transform (Site not responding. Last check: )
		When these half-length transforms are successively decomposed, we are left with the diagram shown in the bottom panel that depicts the length-8 FFT computation.
		Other "fast" algorithms were discovered, all of which make use of how many common factors the transform length N has.
		In over thirty years of Fourier transform algorithm development, the original Cooley-Tukey algorithm is far and away the most frequently used.
	cnx.org /content/m0528/latest (819 words)

	Fast Fourier Transform - Tutorial - Development Library - National Instruments
		First we compute the FFT of the rows of an image and then follow up with the FFT of the columns.
		The second part of the FFT function is the butterflies function.
		Remember that the FFT is not a different transform than the DFT, but a family of more efficient algorithms to accomplish the data transform.
	zone.ni.com /devzone/conceptd.nsf/webmain/A61876074AE0B9918625684600522CF4 (1541 words)

	The Fast Fourier Transform
		The discrete Fourier transform (DFT) of a vector of length
		It is this so-called ``Fast Fourier Transform'' (FFT) which led to a rapid uptake of interest in the method in many applications.
		The FFT algorithm thus reduces the operation count for the Fourier transformation from
	www.dl.ac.uk /TCSC/Subjects/Parallel_Algorithms/FFTreport/node3.html (722 words)

	Cooley tukey fft algorithm - Wikipedia, the free encyclopedia (Site not responding. Last check: )
		Start the Cooley tukey fft algorithm article or add a request for it.
		Look for Cooley tukey fft algorithm in Wiktionary, our sister dictionary project.
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	www.sciencedaily.com /encyclopedia/cooley_tukey_fft_algorithm (161 words)

	Fft - ,Simdesign - Complex mixed-radix FFT on arbitrary length data,FFT Links,fft (MATLAB Functions),Discrete FFT Fast ... (Site not responding. Last check: )
		This library provides a Delphi implementation for a complex Fast Fourier Transform (FFT) on an arbitrary length data series.
		If X is a matrix, fft returns the Fourier transform of each column of the matrix.
		GPFA - Routines for the generalized prime factor fast Fourier transform (written by C. Temperton).
	addyourlinkhere.com /aylh/fft.htm (218 words)

	FFT
		The proportion of sin and cos terms are within the fft are shown as blue and green dots within the power spectrum.
		Since the fft algorithm requires an even number of points, we have chosen to drop the last data point --the point where the function is evaluated as f(max) -- if an odd number of points is specified.
		The FFT routine used in the mathapps.FFT applet uses the jnt.fft package that was developed by Bruce Miller at
	webphysics.davidson.edu /Applets/mathapps/mathapps_fft.html (513 words)

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