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	Willard Gibbs - Wikipedia, the free encyclopedia
		Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis.
		Between 1876 and 1878 Gibbs wrote a series of papers collectively entitled "On the Equilibrium of Heterogeneous Substances", considered one of the greatest achievements in physical science in the 19th century and the foundation of the science of physical chemistry.
		Gibbs was born in New Haven, Connecticut, where his father was a professor of sacred literature at Yale University's Divinity School, best known today for his involvement in the Amistad trial.
	en.wikipedia.org /wiki/Willard_Gibbs (1125 words)

	Gibbs phenomenon -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		The Gibbs phenomenon was first observed by (United States physicist (born in Germany) who collaborated with Morley in the Michelson-Morley experiment (1852-1931)) Albert Michelson via a mechanical graphing machine.
		The phenomenon was first explained mathematically by (Click link for more info and facts about J. Willard Gibbs) J.
		In practice, the difficulties associated with the Gibbs phenomenon can be ameliorated by using a smoother method of Fourier series summation, such as (Click link for more info and facts about Fejér summation) Fejér summation or Riesz summation, or by using (Click link for more info and facts about sigma-approximation) sigma-approximation.
	www.absoluteastronomy.com /encyclopedia/g/gi/gibbs_phenomenon.htm (855 words)

	The Lag Spectrum, Gibbs Phenomenon and Hanning Smoothing
		The Gibbs phenomenon is the ringing at the edges of the frequency spectrum that results from the truncation of the temporal (lag) cross-correlation spectrum.
		When observing with a narrow band and many spectral line channels, of order 128, Gibbs phenomenon is less destructive since the amplitude of the ripple decreases as one moves away from the band edge.
		Gibbs phenomenon is described in Chapters 4 and 18 of SIRA as well.
	www.vla.nrao.edu /astro/guides/sline/current/node11.html (721 words)

	Gibbs phenomenon (Site not responding. Last check: 2007-10-07)
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	www.iownmars.com /gibbs-phenomenon.html (1113 words)

	[REQ] The Gibbs Phenomenon in Fourier Analysis
		This is followed by a few typical illustrations for the appearance of the Gibbs phenomenon in the truncated Fourier series and integrals.
		It also includes other typical methods of filtering, a recent transform method, and some possible advantage of the presence of the Gibbs phenomenon for edge detection purposes, such as determining the locations of shocks, or sharper edges for the magnetic resonance imaging (MRI) of the defective parts of the heart, for example.
		The chapter concludes with attempts at filtering the Gibbs phenomenon, which are, primarily, Fejer averaging (or summability) methods.
	www.edaboard.com /ftopic79063.html (1235 words)

	Amazon.de: English Books: Gibbs Phenomenon in Fourier Analysis, Splines & Wavelet Approximations (Mathematics & ... (Site not responding. Last check: 2007-10-07)
		Covers the basic elements of the Gibbs phenomenon as it appears in various applications where functions with jump discontinuities are represented.
		The author covers the appearance of the Gibbs phenomenon in Fourier analysis, orthogonal expansions, integral transforms, splines and wavelet approximations.
		The work is intended as an introduction for engineering and scientific practitioners in the fields where this phenomenon may appear in their use of various function representations.
	www.amazon.de /exec/obidos/ASIN/0792351096 (316 words)

	Computational Mathematics and Applications Seminar
		Two techniques for the resolution of the Gibbs' phenomenon are discussed, filtering and reprojection methods.
		An adaptive filter with optimal joint time-frequency localization is presented, which recovers a function from its N term Fourier projection within the error bound \exp(-Nd(x)), where d(x) is the distance from the point being recovered to the nearest discontinuity.
		An extension of Gegenbauer postprocessing with improved convergence and robustness properties is presented, the robust Gibbs complements.
	web.comlab.ox.ac.uk /oucl/seminars-ht05/extra/050113.html (209 words)

	On The Gibbs Phenomenon Iv: Recovering Exponential Accuracy In A Sub-Interval From A Gegenbauer Partial Sum Of A ... (Site not responding. Last check: 2007-10-07)
		2: The resolution of the Gibbs phenomenon for spherical harmonics (context) - Gelb - 1997
		Gottlieb and C.-W. Shu, On The Gibbs Phenomenon IV: recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function, Math.
		12 The Gibbs Phenomenon I: recovering exponential accuracy from..
	citeseer.ist.psu.edu /gottlieb95gibbs.html (457 words)

	On the Gibbs Phenomenon and Its Resolution
		The Gibbs phenomenon, as we view it, deals with the issue of recovering point values of a function from its expansion coefficients.
		The main theme here is not the structure of the Gibbs oscillations but the understanding and resolution of the phenomenon in a general setting.
		The purpose of this article is to review the Gibbs phenomenon and to show that the knowledge of the expansion coefficients is sufficient for obtaining the point values of a piecewise smooth function, with the same order of accuracy as in the smooth case.
	epubs.siam.org /sam-bin/dbq/article/30139 (217 words)

	Gibbs Phenomenon
		One shortcoming of Fourier series today known as the Gibbs phenomenon was first observed by H. Wilbraham in 1848 and then analyzed in detail by Josiah W. Gibbs (1839-1903).
		Gibbs got interested to the behavior of the sequence of Fourier partial sums around this point.
		Looking at the graphs of the partial sums, we see that a strange phenomenon is happening.
	www.sosmath.com /fourier/fourier3/gibbs.html (333 words)

	[music-dsp] Gibbs' effect (Site not responding. Last check: 2007-10-07)
		IIRC, the Gibbs effect is a considerably subtler thing, and has to do with the convergence properties of the Fourier integral.
		The particular variation of Gibbs' phenomenon I mean comes about when we deal with an extended version of the Fourier transform, called a Plancherel transform.
		Finally, the Gibbs effect can sometimes be manipulated out of existence by using a different basis in our decomposition (e.g.
	aulos.calarts.edu /pipermail/music-dsp/2002-February/014334.html (823 words)

	Fourier Series Convergence Gibbs (Site not responding. Last check: 2007-10-07)
		The height of the peaks of the oscillation decreases away from the jump, but the height of peak1, peak2 etc remain the same as the number of terms summed increases.
		The effect is referred to as the Gibbs phenomenon and is illustrated by the applet below.
		In the above applet 2 curves are shown summed for different number of terms.
	cnyack.homestead.com /files/afourse/fsgibbs.htm (149 words)

	Electronic Equipment - Beginner DSP questions
		The Gibbs phenomenon is not at all an issue.
		As before, the Gibbs phenomenon in time is the result of truncating its
		phenomenon in frequency is the result of truncating its sampled time series.
	www.electronic1.net /detail-4454609.html (2405 words)

	Radially Symmetric Fourier Transforms (Site not responding. Last check: 2007-10-07)
		Illustrations of the method are presented, and the Gibbs' phenomenon associated with the ROSAT PSPC PRF is discussed.
		As in other Fourier transform techniques it is important to be aware that jumps in the functions, or their derivatives, cause the appearance of the Gibbs' phenomenon.
		Thus the RFT is useful for performing accurate convolutions of arbitrary-length and irregularly-sampled arrays quickly: the 8027-element convolution in Figure 3 used a 1395-point Fourier transform array and took under 10 min on a SPARCstation 2.
	cadcwww.dao.nrc.ca /ADASS/adass_proc/adass3/papers/birkinshawm/birkinshawm.html (540 words)

	Math Mintes page 3 and 4 (Site not responding. Last check: 2007-10-07)
		We applied the elimination of the Gibbs phenomenon technique to noisy spherical data in spectral climate models.
		We have successfully recovered mountain data contaminated by the Gibbs phenomenon, and our current efforts involve creating a robust numerical method that will effectively reduce the Gibbs phenomenon in spectral climate models.
		This research, together with the elimination of the Gibbs phenomenon, makes spectral methods a strong competitor in the arena of numerical methods for solving nonlinear partial differential equations.
	math.la.asu.edu /~math/MathMinutes/3_4.html (2424 words)

	Gibbs Effect (Site not responding. Last check: 2007-10-07)
		Synthesis Imaging Gibbs Phenomenon -- from Eric Weisstein's World of Physics...
		The Lag Spectrum, Gibbs Phenomenon and Hanning Smoothing...
		C 17, 837 (1978): Young and Gibbs - Effect of pion distortion......
	www.scienceoxygen.com /math/231.html (236 words)

	Gibbs phenomenon Info - Bored Net - Boredom (Site not responding. Last check: 2007-10-07)
		Gibbs phenomenon Info - Bored Net - Boredom
		The Gibbs phenomenon, first observed by Albert Michelson via a mechanical graphing machine and first explained by Willard Gibbs, is the peculiar mode in which the Fourier series of a piecewise continuous periodic function f fails to converge uniformly to f.
		At a jump discontinuity of f, the nth partial sum of the Fourier series jumps too far and overshoots its target.
	www.borednet.com /e/n/encyclopedia/g/gi/gibbs_phenomenon.html (98 words)

	Fourier Series and Gibbs Phenomenon Overview (Site not responding. Last check: 2007-10-07)
		For periodic signals with discontinuities, however, such as a periodic square wave, even a large number of harmonics will not be sufficient to reproduce the square wave exactly.
		This effect is known as Gibbs phenomenon and it manifests itself in the form of ripples of increasing frequency and closer to the transitions of the square signal.
		An illustration of Gibbs phenomenon is shown in the figure below.
	www.ee.ucla.edu /~dsplab/fgp/over.html (260 words)

	Gibbs's Phenomena (Site not responding. Last check: 2007-10-07)
		J. Willard Gibbs first explained this phenomenon in 1899, and therefore these discontinuous points are referred to as Gibbs Phenomenon.
		This phenomenon is a specific case of nonuniform convergence.
		For Fourier series, Gibb's phenomenon peaks have finite height and zero width: The error differs from zero only at isolated points--whenever the periodic signal contains discontinuities--and equals about 9% of the size of the discontinuity.
	cnx.rice.edu /content/m10092/latest (1180 words)

	IngentaConnect Gibbs Phenomenon for Wavelets (Site not responding. Last check: 2007-10-07)
		This phenomenon was noticed by Michelson [6] and explained by Gibbs [3] in 1899.
		This phenomenon is known as the Gibbs effect.
		Certain conditions on the size of the wavelet kernel will be examined to determine if a Gibbs effect occurs and what magnitude it is. An if and only if condition for the existence of a Gibbs effect is presented, and this condition is used to prove existence of Gibbs effects for some compactly supported wavelets.
	api.ingentaconnect.com /content/ap/ha/1996/00000003/00000001/art00006 (225 words)

	A Padé-based algorithm for overcoming the Gibbs phenomenon (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		A Padé-based algorithm for overcoming the Gibbs phenomenon (ResearchIndex)
		A Padé-based algorithm for overcoming the Gibbs phenomenon
		21 the Gibbs phenomenon and its resolution (context) - Gottlieb, Shu - 1997
	citeseer.ist.psu.edu /496239.html (322 words)

	Windowing
		One possible appearance of these aliasing artifacts is the Gibbs phenomenon [
		The Gibbs phenomenon is an overshooting of the reconstructed function which appears around discontinuities of the sampled function.
		The appearance of the Gibbs phenomenon can be decreased through a multiplication of the Fourier series representation of the signal with a weighting window function.
	www.cg.tuwien.ac.at /courses/projekte/vis/finished/MArtner/node30.html (328 words)

	Gibbs Phenomenon (Site not responding. Last check: 2007-10-07)
		Gibbs phenomenon is the oscillatory behavior observed when a square wave is reconstructed from a finite number of harmonics.
		The unit cell of the square wave is given by
		Maintained by John Loomis, last updated 30 Aug 2003
	www.engr.udayton.edu /faculty/jloomis/ece561/notes/dft/gibbs.html (97 words)

	Bublos.com: Compare Book Prices ›› Gibbs Phenomenon in Fourier Analysis, Splines, and Wavelet Approximations ... (Site not responding. Last check: 2007-10-07)
		Gibbs Phenomenon in Fourier Analysis, Splines, and Wavelet Approximations - Abdul J. Jerri - Hardcover
		This is the first book dedicated to covering the basic elements of the Gibbs phenomenon as it appears in various applications where functions with jump discontinuities are represented.
		It is presented with detailed analysis and illustrations combined with historical information.
	www.bublos.com /isbn/0792351096.html (696 words)

	The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet (Mathematics and Its Applications) : Entertaining Comments (Site not responding. Last check: 2007-10-07)
		The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet (Mathematics and Its Applications) : Entertaining Comments
		Book / The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet (Mathematics and Its Applications)
		The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet (Mathematics and Its Applications)
	queerpopculture.com /entertainment/asinsearch_0792351096 (70 words)

	Mathematics and Its Applications
		-sense, where the measure of the Gibbs phenomenon depends on p in L
		Illustration of Some Basic Wavelets, their Fourier Transforms and a Glimpse at the Gibbs Phenomenon
		Customers from other countries in the European Community please fill in the VAT number of your institute/company in the appropriate space on the order form; or add 6% VAT to the total amount (customers from the UK are not charged VAT).
	www.clarkson.edu /~jerria/solnman/gibbs.html (1266 words)

	On the Gibbs phenomenon IV recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a ... (Site not responding. Last check: 2007-10-07)
		On the Gibbs phenomenon IV recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function (SuDoc NAS 1.26:194912) - techwritingjobs.com Info and Reviews
		Book / On the Gibbs phenomenon IV recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function (SuDoc NAS 1.26:194912)
		On the Gibbs phenomenon IV recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function (SuDoc NAS 1.26:194912)
	www.techwritingjobs.com /shop/asinsearch_B00010MG56.html (158 words)

	FedorDeRidder.html
		This paper presents a sine wave fitting procedure for characterizing measurements of a harmonic signal in the presence of additive noise and an unknown time base distortion.
		In general the reconstructed time base distortion of the existing solutions [1, 2] suffers from the Gibbs phenomenon (ringing) at the borthers of the data record.
		This paper presents a solution that suppresses the Gibbs phenomenon in the estimated time base distortion without ignoring data samples at the borders.
	elecwww.vub.ac.be /Papers/fedorderidder.htm (751 words)

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