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	Fourier (Site not responding. Last check: 2007-11-07)
		Fourier began teaching at the Collège de France and, having excellent relations with Lagrange, Laplace and Monge, began further mathematical research.
		Fourier was elected secretary to the Institute, a position he continued to hold during the entire French occupation of Egypt.
		Fourier returned to France in 1801 with the remains of the expeditionary force and resumed his post as Professor of Analysis at the École Polytechnique.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Fourier.html (2048 words)

	Lecture 21: The Utopian Socialists: Charles Fourier (1)
		For Fourier, all manual labor was arduous and irksome -- whether in the factory, workshop or field, the plight of the laboring population was intolerably dehumanizing.
		Fourier’s phalanx was to become a self-contained community housing 1,620 members with a myriad of subdivisions designed to encourage a dynamic interplay of various human passions.
		Fourier can also be described as a brilliant exponent of the idea of alienation, a concern which we will find fully developed in Marx, or as an early theoretician of the affluent society, a theme later developed by the American economist, John Kenneth Galbraith.
	www.historyguide.org /intellect/lecture21a.html (2829 words)

	Biography of Jean-Baptiste-Joseph Fourier
		Baron Jean-Baptiste-Joseph Fourier (March 21 1768-May 16, 1830), born in poor circumstances in Auxerre, introduced the idea that an arbitrary function, even one defined by different analytic expressions in adjacent segments of its range (such as a staircase waveform), could nevertheless be represented by a single analytic expression.
		Fourier was appointed as Prefect of Isèe by Napoleon in 1802 after a brief return to his former position as Professor of Analysis at the Ecole Polytechnique in Paris.
		Fourier’s days in provincial government then ended and he moved to Paris to enter a life of science and scientific administration, being elected to the Académie des Sciences in 1817, to the position of permanent secretary in 1823, and to the Académie Française in 1826.
	www.swarthmore.edu /natsci/echeeve1/Ref/Fourier/FourierBio.html (946 words)

	CHAPTER-5 (Site not responding. Last check: 2007-11-07)
		Recall from Chapter 2 that the Fourier transform is a mathematical technique for converting time domain data to frequency domain data, and vice versa.
		A Fourier pair is two functions, the frequency domain form and the corresponding time domain form.
		The second set of Fourier transforms is performed in the t" dimension to yield an f' by f" set of data.
	www.cis.rit.edu /htbooks/nmr/chap-5/chap-5.htm (1199 words)

	Glossary of People: Fo (Site not responding. Last check: 2007-11-07)
		Fourier drew upon the French materialists on the role of environment and education in moulding personality.
		Fourier takes the bourgeoisie, their inspired prophets before the Revolution, and their interested eulogists after it, at their own word.
		"Fourier is not only a critic, his imperturbably serene nature makes him a satirist, and assuredly one of the greatest satirists of all time.
	www.marxists.org /glossary/people/f/o.htm (899 words)

	Chapter 11: The Fourier Transform
		The methods of Fourier analysis described in previous chapters have as their domain three classes of functions: discrete data vectors with finite number of values, discrete vectors with infinite number of values, and continuous functions which are confined to a finite interval.
		This is the province of the Fourier Transform.
		Although the preceding development is useful for developing an intuitive understanding of the transition from Fourier series to the Fourier transform, the actual results are largely of historical interest since modern authors invariably choose to represent the Fourier transform in complex form.
	research.opt.indiana.edu /Library/FourierBook/ch11.html (1590 words)

	Fourier and the theory of heat (Site not responding. Last check: 2007-11-07)
		By 1800, alternatives to the caloric hypothesis appeared and, in 1811, Joseph Fourier (1768-1830) published a mathematical theory of heat conduction that was entirely independent of the caloric hypothesis.
		Fourier's first step was to avoid speculation about "caloric." In this way, Fourier set the study of the theory of heat in the tradition of rational mechanics, basing it on differential equations that characterized the transmission of heat, equations that were independent of all physical hypotheses.
		The heat transmitted between two molecules was proportional to the difference in their temperature and a function of the distance between them, which of course varied with the nature of the intervening substance.
	www.victorianweb.org /science/fourier.html (462 words)

	KR Mathematics: Fourier Transformations (Site not responding. Last check: 2007-11-07)
		A fourier series works on the idea that any wave function, such as a wave pulse can be constructed by a combination of pure frequency waves, such as a sine or cosine.
		Doing Fourier Transformations by hand can be very tedious, but with the invention of computers programs and algorithms were developed to preform fourier transformations at a quicker rate.
		Fourier transformations are a nice mathematical tool for looking at wave functions and retrieving information from a wave function.
	www.kopernekus.com /math/fourier.asp (729 words)

	An Intuitive Explanation of Fourier Theory (Site not responding. Last check: 2007-11-07)
		Fourier theory states that any signal, in our case visual images, can be expressed as a sum of a series of sinusoids.
		The significant point is that the Fourier image encodes exactly the same information as the brightness image, except expressed in terms of amplitude as a function of spatial frequency, rather than brightness as a function of spatial displacement.
		Conversely, parallel rays from the entire input image are focused onto the single central point of the Fourier image, where it defines the central DC term by the average brightness of the input image.
	cns-alumni.bu.edu /~slehar/fourier/fourier.html (1958 words)

	Fourier transform -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		This is actually the inverse continuous Fourier transform, whereas the Fourier transform expresses F(ω) in terms of f(t); the original function and its transform are sometimes called a transform pair.
		The (The property of relative size or extent) magnitude of the resulting complex-valued function F represents the (Greatness of magnitude) amplitudes of the respective frequencies (ω), while the (Click link for more info and facts about phase shift) phase shifts are given by arctan(imaginary parts/real parts).
		However, it is important to realize that Fourier transforms are not limited to functions of time, and temporal frequencies.
	www.absoluteastronomy.com /encyclopedia/f/fo/fourier_transform.htm (990 words)

	No. 186: Jean Baptiste Joseph Fourier
		Fourier did all sorts of negotiation and administration during the Egypt campaign.
		Fourier's intuition led him where his logic couldn't always follow.
		Joseph Fourier Savant et Préfet 1768-1830, Grenoble: Bibliotheques Municipales, 1989.
	www.uh.edu /admin/engines/epi186.htm (494 words)

	Jean Baptiste Joseph Fourier (Site not responding. Last check: 2007-11-07)
		Later in 1794, Fourier was nominated to study at the Ecole Normale in Paris.
		Fourier was elected to the Académie des Sciences in 1817, and served as secretary to the mathematical section.
		Fourier resumed his mathematical researches and published a number of papers, some in pure mathematics while some were on applied mathematical topics.
	www.stetson.edu /~efriedma/periodictable/html/Fe.html (643 words)

	Fourier transform theory
		The Fourier transform is simply a method of expressing a function (which is a point in some infinite dimensional vector space of functions) in terms of the sum of its projections onto a set of basis functions.
		A graph of the amplitude of the Fourier components is known as the spectrum of the wave form.
		The Fourier transform describes a way of decomposing a function into a sum of orthogonal basis functions in just the same way as we decompose a point in Euclidean space into the sum of its basis vector components.
	homepages.inf.ed.ac.uk /rbf/CVonline/LOCAL_COPIES/OWENS/LECT4/node2.html (1260 words)

	Fourier Cosine Series (Site not responding. Last check: 2007-11-07)
		There are three distinct versions of the Fourier series in common use, the "full" Fourier series, the Fourier sine series, and the Fourier cosine series.
		For this reason, different sets of Fourier functions will arise in our study of partial differential equations, depending on which kind of "boundary conditions" which are physically appropriate for a given problem.
		Just as for the full Fourier series, the Fourier sine functions are a complete set, and they satisfy some useful identities, which I have collected in a theorem (which is almost identical to the one for the full series).
	www.math.gatech.edu /~harrell/pde/cosine.html (724 words)

	Fourier Analysis (Site not responding. Last check: 2007-11-07)
		Then, since Fourier analysis allows us to redefine the signals in terms of sinusoids, all we need to do is determine how any given system effects all possible sinusoids (its transfer function) and we have a complete understanding of the system.
		Furthermore, since we are able to define the passage of sinusoids through a system as multiplication of that sinusoid by the transfer function at the same frequency, we can convert the passage of any signal through a system from convolution (in time) to multiplication (in frequency).
		The four Fourier transforms that comprise this analysis are the Fourier Series, Continuous-Time Fourier Transform, Discrete-Time Fourier Transform and Discrete Fourier Transform.
	cnx.rice.edu /content/m10096/latest (372 words)

	Fast Fourier Transform (FFT)
		Fourier transforms are also used to solve partial differential equations.
		Example results obtained with fast Fourier transform software are compared with the actual Fourier transform of function [3].
		Apostol (1974) is a masterful mathematics text that covers the theory of Fourier transforms.
	www.riskglossary.com /articles/fast_fourier_transform.htm (953 words)

	Joseph Fourier
		Fourier returned to France in 1801 with the remains of the expeditionary force and resumed his post as Professor of Analysis at the Ecole Polytechnique.
		Fourier was elected to the Académie des Sciences in 1817.
		A C Bose, Fourier series and its influence on some of the developments of mathematical analysis, Bulletin of the Calcutta Mathematical Society 9 (1917-8), 71-84.
	www.shsu.edu /~icc_cmf/bio/fourier.html (2204 words)

	Fourier Sine Series (Site not responding. Last check: 2007-11-07)
		For this reason, different sets of Fourier functions will arise in our study of partial differential equations, depending on which kind of boundary conditions are physically appropriate for a given problem.
		The full Fourier series consists of functions which are periodic , and are particularly good for representing or approximating periodic functions, that is, functions for which f(x + L) = f(x).
		The Fourier sine series, in contrast, is well adapted to functions which are zero at x=0 and x=L, since all the functions sin(n \pi x/L) have this property.
	www.math.gatech.edu /~harrell/pde/sine.html (584 words)

	Fourier Series (Site not responding. Last check: 2007-11-07)
		Fourier series are made up of sinusoids, all of which have frequencies that are integer multiples of some fundamental frequency.
		A great thing about using Fourier series on periodic functions is that the first few terms often are a pretty good approximation to the whole function, not just the region around a special point.
		Fourier series are used extensively in engineering, especially for processing images and other signals.
	mathforum.org /key/nucalc/fourier.html (176 words)

	CHAPTER-5 (Site not responding. Last check: 2007-11-07)
		The concept of a Fourier transform is not that difficult to understand.
		The Fourier transform (FT) process is like the musician hearing a tone (time domain signal) and determining what note (frequency) is being played.
		The inverse Fourier Transform (IFT) is like the musician seeing notes (frequencies) on a sheet of music and converting them to tones (time domain signals).
	www.cis.rit.edu /htbooks/mri/chap-5/chap-5.htm (1561 words)

	Fourier Series
		Such a Fourier expansion provides an interpetation of the wave in terms of its elementary components.
		An unknown wave function is to be expanded as a linear combination of well known wave functions and the problem is re-formulated to find the expansion coefficients.
		But if f(x) itself is periodic then its Fourier expansion, F(x), obtained on one period of the function represents it over all periods.
	www.sci.wsu.edu /idea/quantum/fourier_series.htm (561 words)

	Harmonic Phasors and Fourier Series
		Various forms of the Fourier series description for periodic signals are based on alternate ways of writing a cosine signal.
		Notice that as more terms are added to the Fourier series, the overshoot near the discontinuity decreases only slightly in amplitude, though it decreases significantly in duration.
		A more extreme case is the impulse train, where the Fourier series coefficients remain constant and the mathematical nature of convergence of the series is far from apparent.
	www.jhu.edu /~signals/phasorlecture (788 words)

	The educational encyclopedia, Fourier javaapplets, Fourier java applets, building a wave shape from sines and cosines (Site not responding. Last check: 2007-11-07)
		Fourier decomposition building a wave shape from sines and cosines, Fourier composition of a square wave, Fourier composition of a traingle wave, Fourier composition of a sawtooth wave, Fourier composition of a pulse train, Signal generation with Fourier analysis
		Fourier series applet a method of expressing an arbitrary periodic function as a sum of cosine terms.
		Fourier transforms the Fourier transform defines a relationship between a signal in the time domain and its representation in the frequency domain.
	users.telenet.be /educypedia/electronics/javafourier.htm (327 words)

	Jean Baptiste Joseph Fourier (1768 - 1830) (Site not responding. Last check: 2007-11-07)
		Jean Baptiste Joseph Fourier was born at Auxerre on March 21, 1768, and died at Paris on May 16, 1830.
		After the British victories and the capitulation of the French under General Menou in 1801, Fourier returned to France, and was made prefect of Grenoble, and it was while there that he made his experiments on the propagation of heat.
		Fourier left and unfinished work on determinate equations which was edited by Navier, and published in 1831; this contains much original matter, in particular there is a demonstration of Fourier's theorem on the position of the roots of an algebraical equation.
	www.maths.tcd.ie /pub/HistMath/People/Fourier/RouseBall/RB_Fourier.html (477 words)

	Image Transforms - Fourier Transform
		The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components.
		The DFT is the sampled Fourier Transform and therefore does not contain all frequencies forming an image, but only a set of samples which is large enough to fully describe the spatial domain image.
		Because the image in the Fourier domain is decomposed into its sinusoidal components, it is easy to examine or process certain frequencies of the image, thus influencing the geometric structure in the spatial domain.
	homepages.inf.ed.ac.uk /rbf/HIPR2/fourier.htm (2172 words)

	AllRefer.com - Charles Fourier (Political Science, Biography) - Encyclopedia
		Members would live in the phalanstEre (or phalanstery), a community building, and work would be divided among people according to their natural inclinations.
		Fourier was not ready to discard capitalism completely; basically his ideal was an agricultural society, systematically arranged.
		After Fourier's death his principal disciple, Victor Prosper ConsidErant, tried to found a colony in Texas.
	reference.allrefer.com /encyclopedia/F/FourierC.html (375 words)

	Charles Fourier
		Charles Fourier was born in Besancon, France, on 7th April, 1773.
		Fourier suggested that these communes should contain about 1,600 people and should attempt to be compatible with each member's "natural talents, passions, and inclinations".
		Although no long-term phalanxes were established, Fourier's ideas influenced a generation of socialists, anarchists, feminists, pacifists, internationalists and others questioning the morality of the capitalist system.
	www.spartacus.schoolnet.co.uk /RUSfourier.htm (292 words)

	Fourier Transforms
		A common operation in analyzing various kinds of data is to find the Fourier transform, or spectrum, of a list of values.
		In different scientific and technical fields different conventions are often used for defining discrete Fourier transforms.
		Two-dimensional Fourier transforms are often used in image processing.
	documents.wolfram.com /v4/MainBook/3.8.3.html (205 words)

	Discrete Fourier Transform (Site not responding. Last check: 2007-11-07)
		Algorithm 545 [Fra79] of the Collected Algorithms of the ACM is an implementation of the fast Fourier transform optimizing virtual memory performance and written in Fortran.
		Notes: Brigham [Bri74] is an excellent introduction to Fourier transforms and the FFT and is strongly recommended, as is the exposition in [PFTV86].
		Credit for inventing the fast Fourier transform is usually given to Cooley and Tukey [CT65], although it is not completely deserved.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE146.HTM (925 words)

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