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	John Tukey - Wikipedia, the free encyclopedia
		Tukey obtained a Bachelor of Science degree in 1936 and a Master of Science degree in chemistry in 1937 from Brown University before moving to Princeton University to study for his doctorate in mathematics.
		Tukey coined many statistical terms that have become part of common usage, but the two most famous coinages attributed to him were related to computer science.
		Tukey used the term "software" in a computing context in a 1958 article and this may have been the first published use.
	en.wikipedia.org /wiki/John_W._Tukey (494 words)

	Cooley-Tukey FFT algorithm - Wikipedia, the free encyclopedia
		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).
		Tukey reportedly came up with the idea during a meeting of a US presidential advisory committee discussing ways to detect nuclear-weapon tests in the Soviet Union (Rockmore, 2000).
		Cooley and Tukey's 1965 paper reported a running time of 0.02 minutes for a size-2048 complex DFT on an IBM 7094 (probably in 36-bit single precision, ~8 digits).
	en.wikipedia.org /wiki/Cooley-Tukey_FFT_algorithm (2264 words)

	Physics Today July 2001
		Born on 16 June 1915 in New Bedford, Massachusetts, Tukey received an ScB in chemistry (1936) and an ScM in chemistry (1937) from Brown University and an MA in mathematics (1938) and a PhD in mathematics (1939) from Princeton University.
		Tukey is credited with the first printed use of the word "software" to refer to computer programs; he observed that the software might well prove to become more valuable than the hardware.
		Tukey tried to interest several of his colleagues in pursuing his notions on the redundancy in the arithmetic of the Fourier series.
	physicstoday.org /pt/vol-54/iss-7/p80.html (812 words)

	Biography of John W. Tukey
		John Tukey has attracted international attention for his studies in mathematical and theoretical statistics and their applications to a wide variety of scientific and engineering disciplines.
		Tukey served as chairman of the Technical Advisory Committee of the National Assessment of Educational Progress (NAEP) from its inception in 1963 and throughout its operation by the Education Commission of the States (which ended in 1982).
		Tukey has taught on both the undergraduate and graduate levels and is widely sought as a seminar leader and lecturer.
	cm.bell-labs.com /cm/ms/departments/sia/tukey/bio.html (1333 words)

	John Tukey (Site not responding. Last check: 2007-11-01)
		John Wilder Tukey (June 16, 1915 - July 26, 2000) was a statistician.
		Born New Bedford, Massachusetts, Tukey obtained a Bachelor of Science degree in 1936 and a Master of Science degree in chemistry in 1937 from Brown University before moving to Princeton University to study for his doctorate in mathematics.
		Retiring in 1985, Tukey died in New Brunswick, New Jersey.
	www.freedownloadsoft.com /info/john-w-tukey.html (275 words)

	The FFT: Making Technology Fly
		Cooley takes pains to praise the Gentleman-Sande paper, as well as an earlier paper by Sande (who was a student of Tukey's) that was never published.
		In fact, Cooley says, the Cooley-Tukey algorithm could well have been known as the Sande-Tukey algorithm were it not for the "accident" that led to the publication of the now-famous 1965 paper.
		As he recounts it, the paper he co-authored with Tukey came to be written mainly because a mathematically inclined patent attorney happened to attend the seminar in which Cooley described the algorithm.
	www.siam.org /siamnews/mtc/mtc593.htm (1915 words)

	Fast Fourier transform (Site not responding. Last check: 2007-11-01)
		This method (and the general idea of an FFT) was popularized by a publication of J. Cooley and J. Tukey in 1965, but it was later discovered that those two authors had independently re-invented an algorithm known to Carl Friedrich Gauss around 1805 (and subsequently rediscovered several times in limited forms).
		The most well-known use of the Cooley-Tukey algorithm is to divide the transform into two pieces of size n/2 at each step, and is therefore limited to power-of-two sizes, but any factorization can be used in general (as was known to both Gauss and Cooley/Tukey).
		To verify the correctness of an FFT implementation, rigorous guarantees can be obtained in O(n log n) time by a simple procedure checking the linearity, impulse-response, and time-shift properties of the transform on random inputs (Ergün, 1995).
	bopedia.com /en/wikipedia/f/fa/fast_fourier_transform.html (1450 words)

	Cooley-Tukey FFT algorithm (Site not responding. Last check: 2007-11-01)
		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).
		Because the Cooley-Tukey algorithm breaks the DFT into smaller DFTs, it can be combined arbitrarily with any other algorithm for the DFT.
		The more modern FFT library FFTW, on a 2GHz Pentium 4 in 64-bit double precision (~16 digits), can compute a size-64 real-input DFT in 0.5μs and a size-2048 complex DFT in 50μs, speedups of about 16,000,000,000 and 20,000 over Danielson and Lanczos and Cooley and Tukey, respectively, not even including the considerable improvements in accuracy.
	bopedia.com /en/wikipedia/c/co/cooley_tukey_fft_algorithm.html (2146 words)

	John Tukey: ZoomInfo Business People Information (Site not responding. Last check: 2007-11-01)
		John Tukey's summary was automatically generated using 7 references found on the Internet.
		John Tukey is a pioneer in exploratory data analysis.
		John Tukey and his colleagues studied the "point clouds" that arise in such situations and manipulated them on a computer screen until patterns emerged that indicated relationships among different variables.
	www.zoominfo.com /directory/Tukey_John_4315570.htm (355 words)

	FFT HISTORY
		While James Cooley and John Tukey developed the FFT algorithm.
		Even with the advent of the digital computer the techniques to reduce computational time were generally unknown until 1965 when James W. Cooley and John W. Tukey published their mathematical algorithm which has become known as the fast Fourier transform (FFT) [13].
		Cooley, a relatively new member of the staff, was given the problem because to his own admission "had nothing important to do"[13] and quickly worked it out.
	me.oregonstate.edu /classes/me452/winter95/ButlerKeithMurphy/insth.html (684 words)

	Fast Fourier Transform
		This process is an example of the general technique of divide and conquer algorithms; in many traditional implementations, however, the explicit recursion is avoided, and instead one traverses the computational tree in breadth-first fashion.
		Rescaling the time by n log n, this corresponds roughly to a speedup factor of around 800,000.
		The more modern FFT library FFTW, on a 2GHz Pentium-IV in 64-bit double precision (~16 digits), can compute a size-64 real-input DFT in 1μs and a size-2048 complex DFT in 100μs, speedups of about 8,000,000,000 and 10,000 over Danielson and Lanczos and Cooley and Tukey, respectively, not even including the considerable improvements in accuracy.
	www.ebroadcast.com.au /lookup/encyclopedia/ff/FFT.html (2315 words)

	Cooley and Tukey FFT paper is a Citation Classic (Site not responding. Last check: 2007-11-01)
		Cooley and Tukey FFT paper is a Citation Classic
		NA Digest readers may be interested to know that a ``Citation Classic commentary'' has been published by Cooley and Tukey describing the background to their 1965 paper ``An Algorithm for the Machine Calculation of Complex Fourier Series'' \cite{coto93}.
		This paper, which describes the fast Fourier transform, is one of the most-cited papers in mathematics and computer science, as measured by the Science Citation Index.
	www.csc.fi /math_topics/Mail/NANET94/msg00061.html (132 words)

	In Memoriam: John Wilder Tukey June 16, 1915--July 26, 2000. \| Technology from AllBusiness.com (Site not responding. Last check: 2007-11-01)
		Tukey's contributions to science, and to this journal in particular, were vast, profound, and remarkably farsighted.
		Whole areas of statistics have their foundations laid and others are inspired--spectrum estimation, multiple comparisons, quick and dirty methods, exploratory data analysis, graphics, robust methods, and Monte Carlo.
		The list of applications to science and technology goes on and on: seismology, education, band spectroscopy, halothane, federal statistics, indexing, astrophysics, the Kinsey report, pollution, molecular physics, and halocarbons are a small part of the list.
	www.allbusiness.com /periodicals/article/808081-1.html (478 words)

	John W. Tukey's work on time series and spectrum analysis, David R. Brillinger
		The contributions of John W. Tukey to time series analysis, particularly spectrum analysis, are reviewed and discussed.
		Much of Tukey's early work on spectrum analysis remained unpublished for many years, but the 1959 book by Blackman and Tukey made his approach accessible to a wide audience.
		The time series work of Tukey and others led to the appearance of kernel and nonparametric estimation in mainstream statistics and to the recognition of the consequent difficulties arising in naive uses of the techniques.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aos/1043351248 (1057 words)

	FAST FOURIER ANALYZER - United States Patent 3,581,078
		Additionally, this invention relates to the derivation of the complex Fourier series representation of a selected signal segment from the amplitudes and phases of the harmonically-related frequency components constituting this series.
		James W. Cooley and John W. Tukey, in an article entitled "An Algorithm for the Machine Calculation of Complex Fourier Series," published Apr. 1965 in the Mathematics of Computation, Vol.
		It should be noted that although there are eight nodes in row 3, nodes 011, 101 and 111, row 3, produce output signals which represent the complex conjugates of the second, third and first harmonics, respectively.
	xrint.com /patents/us/3581078 (4913 words)

	Notes on the FFT
		An outline and discussion of his theorems can be found in [18] as well as [8, 9, 1 0, 11].
		Efficient FFT algorithms for length-2M were described by Gauss and discovered in modern times by Cooley and Tukey [27].
		[23] J. Cooley, "The structure of FFT algorithms," April 1990.
	www.fftw.org /burrus-notes.html (3224 words)

	[No title]
		An outline and discussion of his theorems can be found in [17] as well as [7,8,9,10].
		Efficient FFT algorithms for length-2M were described by Gauss and discovered in modern times by Cooley and Tukey [24].
		[20] J. Cooley, "The structure of FFT algorithms," April 1990.
	faculty.prairiestate.edu /skifowit/fft/fftnote.txt (2811 words)

	Cooley-Tukey FFT on the Connection Machine - Johnsson, Krawitz (ResearchIndex)
		If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
		Abstract: We describe an implementation of the Cooley Tukey complex-to-complex FFT on the Connection Machine.
		The implementation is designed to make effective use of the communications bandwidth of the architecture, its memory bandwidth, and storage with precomputed twiddle factors.
	citeseer.ist.psu.edu /johnsson91cooleytukey.html (555 words)

	Fast Fourier Transform (Site not responding. Last check: 2007-11-01)
		FFTs were first discussed by Cooley and Tukey (1965), although
		Brigham, E. The Fast Fourier Transform and Applications.
		Cooley, J. and Tukey, O. ``An Algorithm for the Machine Calculation of Complex Fourier Series.'' Math.
	www.math.sdu.edu.cn /mathency/math/f/f044.htm (391 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		Amazingly, Carl Friedrich Gauss knew of this algorithm for splitting DFTs around 1805.
		It is agreed that Cooley and Tukey reinvented this algorithm independently and included the crucial analysis to show its O(nlgn) complexity.
		Still, why all Gauss’ works haven't been compiled and annotated all in one easily accessible space is beyond me. It seems a lot of time would be saved by simply searching his accomplishments.
	www.ittc.ku.edu /~jgauch/teaching/740.f05/summaries/FFT.doc (335 words)

	FFT - Fast Fourier Transform (Site not responding. Last check: 2007-11-01)
		The Fast Fourier transform is a DFT algorithm developed by Tukey and Cooley in 1965 which reduces the number of computations from something on the order of N
		There are basically two types of Tukey-Cooley FFT algorithms in use: decimation-in-time and decimation-in-frequency.
		This page last modified on Jun 3, 1999.
	www.cs.sunysb.edu /~algorith/implement/FFT/implement.shtml (84 words)

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