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Topic: Mellin transform

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	Correlation methods and apparatus utilizing mellin transforms - Patent 4073010
		By altering the distance from the input plane to the Fourier transform plane, the scale of the Fourier transform is varied.
		The importance of the Mellin transform is thus found in the fact that the magnitude of the Mellin transforms of two functions that are different in scale are equal.
		The inverse Mellin transform is equivalent to the inverse Fourier transform of the logarithmically scaled function.
	www.freepatentsonline.com /4073010.html (3862 words)

	Device for scanning objects by means of ultrasound echography - Patent 4762132
		(D) a processing device (140) for processing the output signal of the arithmetic circuit (132) for calculating the inverse Mellin transform for the display of images of the region scanned and/or data which are representative of the region scanned.
		The processing device 130 itself includes a multiplier circuit 131 for multiplying the restrictive output signals of the transformation devices 110 and 120, and an arithmetic circuit 132 for calculating the inverse Mellin transform of the signal resulting from this multiplication.
		In the processing device which is associated, for example with one of the previously described transformation devices for the transformation of the echographic signal and with the transformation device described above for transforming the attenuation function, the arithmetic circuit for calculating the inverse Mellin transform may be constructed as follows.
	www.freepatentsonline.com /4762132.html (2436 words)

	RAND \| Research Memoranda \| Numerical Solutions of Functional Equations by Means of Laplace Transform--VII : The Mellin ...
		One of a series of Memoranda which have so far considered various analytic and computational aspects of the numerical inversion of the Laplace transform and, in addition, some applications to scientific problems.
		This Memorandum considers the question of the numerical inversion of the Mellin transform.
		This transform also plays an important role in the study of functional equations of the type that arise in mathematical physics.
	www.rand.org /pubs/research_memoranda/RM4179 (251 words)

	The Scaling of Physical Quantities and Its Relation to the Power Spectrum of the Mellin Transform. (Site not responding. Last check: )
		Abstract : Just as one uses the power spectrum of the Fourier transform of data given as a function of a one-dimensional variable to find periodicities in the translation of the variable, one may use the power spectrum of the Mellin transform to find periodicities in the magnification.
		The relation of the Fourier transform to the Mellin transform is discussed, and a theorem of the Wiener-Khinchine type is presented.
		The use of the Mellin transform, offers a new method of extracting meaningful features from data, particularly when the data is noisy.
	stinet.dtic.mil /oai/oai?&verb=getRecord&metadataPrefix=html&identifier=AD0774029 (177 words)

	Mellin biography
		Hjalmar Mellin, the son of a clergyman, was born in Liminka, northern Ostrobothnia, in Finland in 1854.
		Mellin was one of the founders of the
		Mellin's research work was principally in the area of the theory of functions which resulted from the influence of his teachers Mittag-Leffler and Weierstrass.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Mellin.html (550 words)

	[No title]
		Subject: Re: Fourier Transform - Sort Of Date: Fri, 18 Aug 2000 16:01:04 +0200 Newsgroups: sci.math Summary: [missing] > Since the posting of the message you quote, I have been given a lead > on transforms that selects frequency values as human hearing does: > the Mellon Transform and the Fast Mellon Transform.
		I have a bookmarks file started for transformations at http://eznet.net/~progress/dl/trans.htm The last few entries lead to Mellin Transform references.
		I now find out that the connection to wavelet transforms is only that a professor thinks that there is a certain similarity or common thread of reasoning.
	www.math.niu.edu /~rusin/known-math/00_incoming/transforms (340 words)

	SPIE Bookstore
		The Fourier transform, while being suited to solving boundary-value problems, is basic to the frequency spectrum analysis of time-varying waveforms.
		The purpose of this text is to introduce the use of integral transforms in obtaining solutions to problems governed by ordinary and partial differential equations and certain types of integral equations.
		The use of an integral transform is somewhat analogous to that of logarithms.
	bookstore.spie.org /index.cfm?fuseaction=DetailVolume&volume=PM66 (734 words)

	fmt
		The Mellin transform is invariant in modulus to dilations, and decomposes the signal on a basis of hyperbolic signals.
		is the Fourier transform of the analytic signal corresponding to
		The fast Mellin transform is used, for example, in the computation of the affine time-frequency distributions.
	gdr-isis.org /tftb/refguide/node32.html (187 words)

	Chapter 2 Notes
		Laplace transformation belongs to a class of analysis methods called integral transformation which are studied in the field of operational calculus.
		These methods include the Fourier transform, the Mellin transform, etc. In each method, the idea is to transform a difficult problem into an easy problem.
		The one-sided Laplace transform which we are used to is defined by equation (2.1), and is valid over the interval [0,[[infinity]]).
	web.umr.edu /~stutts/Laplace/Laplace.html (2927 words)

	Numerical inversion of real-valued Laplace transforms. Regularization method by Vladimir Kryzhniy
		Analytical background of the method of inverse Laplace transformation made it possible to overcome the known limitations for the problem of exponential analysis.
		This is due to the fact that zeroes of the inverse Laplace transform of a sum of exponential decays are as informative as its maxima.
		The constructed operator is applicable to a certain subset of Laplace transforms.
	www-users.cs.umn.edu /~yelena/web/mathmethod.php (920 words)

	Image Processing Tools (Site not responding. Last check: )
		The Fourier-Mellin transform is a useful mathematical tool for image recognition because its resulting spectrum is invariant in rotation, translation and scale.
		The Fourier Transform itself (FT) is translation invariant and its conversion to log-polar coordinates converts the scale and rotation differences to vertical and horizontal offsets that can be measured.
		A second FFT, called the Mellin transform (MT) gives a transform-space image that is invariant to translation, rotation and scale.
	students.ee.sun.ac.za /~riaanvdd/image_processing_tools.htm (212 words)

	Fourier-sharpreg-firstorder.nb
		Study of the Mellin transform of the velocity field with sharp cut-off and of the first order interaction vertex for the passive scalar
		Reconstruction of the Mellin transform of the velocity correlation
		An overall MINUS sign is introduced in order to compute the Mellin transform of the structure function.
	www.math.helsinki.fi /mathphys/paolo_files/passive_scalar/Fourier-sharpreg-firstorder.html (146 words)

	MATLAB Central File Exchange - Fourier-Mellin based Image Registration (with GUI)
		This GUI implementation of the Fourier-Mellin transform allows registration of an image with respect to a base image.
		Translation, rotation and scale shift values are retrieved and used to form a registered reconstruction.
		The FMT cannot do the template matching where the pattern template only contains an object in the input image and it is much smaller than the input image, but the input image contains many other things in addition to the object contained in the template.
	www.mathworks.com /matlabcentral/fileexchange/loadFile.do?objectId=3000&objectType=FILE (381 words)

	A Comparison of the Two-Sided Laplace Transform and the Mellin Transform - Storming Media
		A Comparison of the Two-Sided Laplace Transform and the Mellin Transform
		From that point of view, the two-sided Laplace transform and the Mellin transform are different representations of the same transform.
		This allows us to easily derive the properties of the Mellin transform from the properties of the two-sided Laplace transform.
	www.stormingmedia.us /57/5719/A571913.html (113 words)

	Fast Evolution of Parton Distributions: pdf Namespace Reference
		Evaluation of the inverse Mellin transform for singlet parton distributions with QED effects with a Gauss-Laguerre quadrature formula with 20 points.
		Evaluation of the inverse Mellin transform for singlet parton distributions with QED effects with a Gauss-Laguerre quadrature formula with 3 points.
		Evaluation of the inverse Mellin transform for singlet parton distributions with QED effects with a Gauss-Laguerre quadrature formula with 30 points.
	wwwthep.physik.uni-mainz.de /~stefanw/partonevolution/namespacepdf.html (984 words)

	The inverse Mellin Transform (Site not responding. Last check: )
		I know that in inverse Laplace Transforms, c is any real number large enough that all the residues of F(s) lie to the left of the contour on the complex plane, but this is not necessarially the case with Mellin Transforms.
		The Mellin transform is essentially a two sided Laplace transform.
		In the latter case, the (Laplace) transform exists if the function being transformed is "of exponential order" meaning that Re(s) > b (some number so contour is to the right of all the poles) has to be sufficiently large to provide convergence in the inverse transform.
	www.physicsforums.com /showthread.php?t=97527 (382 words)

	Mellin-transform information extractor for vibration sources (US6675140)
		extracting features of said input signal by performing a Mellin transform on the output of said wavelet-transforming step in synchrony with periodicity or pseudo-periodicity of said input signal.
		"A Mathematical Framework for Auditory Processing: A Mellin Transform of a Stabilized Wavelet Transform?", by Irino et al., ATR Technical Report, Jan. 29, 1999.
		"A `Gammachirp` Function as an Optimal Auditory Filter with the Mellin Transform", by Irino, IEE ICASSP96, May 7-10, 1996, pp.
	www.delphion.com /details?pn10=US06675140 (469 words)

	FeynCalc Reference Guide: InverseMellin
		InverseMellin[exp, y] performs the inverse Mellin transform of polynomials in OPEm.
		The inverse transforms are not calculated but a table-lookup is done.
		Below is a list of all built-in basic inverse Mellin transforms.
	www.feyncalc.org /FeynCalcBook/InverseMellin (63 words)

	The Convolution Transform
		In studies of general operators of the same nature, general convolution transforms are immediately encountered as the objects of inversion.
		The relation between differential operators and integral transforms is the basic theme of this work.
		Also includes Mellin transform method and less elementary aspects of the method of steepest descents.
	store.doverpublications.com /048644175x.html (181 words)

	Multiscale computing -- Kobayashi et al. 98 (22): 12344 -- Proceedings of the National Academy of Sciences
		Two other important topics associated with wavelets are filter banks (3) and operator theory (4).
		Mellin transform is used to rescale human speech signals.
		denotes the Fourier transform of the wavelet and
	www.pnas.org /cgi/content/full/98/22/12344 (1622 words)

	On the Mellin transform of a product of hypergeometric functions
		On the Mellin transform of a product of hypergeometric functions
		We obtain representations for the Mellin transform of the product of generalized hypergeometric functions
		The later transform is a generalization of the discontinuous integral of Weber and Schafheitlin; in addition to reducing to other known integrals (for example, integrals involving products of powers, Bessel and Lommel functions), it contains numerous integrals of interest that are not readily available in the mathematical literature.
	anziamj.austms.org.au /V40/part2/Miller.html (125 words)

	Philippe Flajolet's Research Papers
		Mellin Transforms and Asymptotics : Harmonic Sums, P.
		Mellin Transforms and Asymptotics : Finite Differences and Rice's Integrals (117kb), P.
		Mellin Transforms and Asymptotics : The Mergesort Recurrence (104kb), P.
	pauillac.inria.fr /algo/flajolet/Publications/publist.html (4526 words)

	The Mellin Transform
		A.; and Marichev, O. Evaluation of Integrals and the Mellin Transform.
		Bracewell's book ("The Fourier Transform and its Applications") has a brief section on the Mellin transform.
		The connection is closer when one realizes that the MT of a signal can be computed by sampling it at exponentially spaced intervals and then computing its Fourier transform.
	perso.orange.fr /polyvalens/clemens/transforms/mellin/mellin.html (410 words)

	Mellin Transform Based Performance Analysis of Fast Frequency Hopping Using Product Combining - ECS EPrints Repository
		Mellin Transform Based Performance Analysis of Fast Frequency Hopping Using Product Combining - ECS EPrints Repository
		Ahmed, S., Yang, L. and Hanzo, L. Mellin Transform Based Performance Analysis of Fast Frequency Hopping Using Product Combining.
		EPrints is free software developed by the University of Southampton to facilitate Open Access to research.
	eprints.ecs.soton.ac.uk /12634 (118 words)

	The Wavelet Digest :: View topic - Preprint: Wavelet filtering with the Mellin transform
		The Wavelet Digest :: View topic - Preprint: Wavelet filtering with the Mellin transform
		Subject: Preprint: Wavelet filtering with the Mellin transform
		Author: Gerald Kaiser, University of Massachusetts at Lowell
	www.wavelet.org /phpBB2/viewtopic.php?t=3138 (123 words)

	RR-3089 : Analysis of an Asymmetric Leader Election Algorithm
		We establish precise asymptotics for the first two moments, and show that the asymptotic expression for the duration of the algorithm exhibits some periodic fluctuations and consequently no limiting distribution exists.
		These results are proved by analytical techniques of the precise analysis of algorithms such as: analytical poissonization and depoissonization, Mellin transform, and complex analysis.
		On établit des asymptotiques précis pour les deux premiers moments, on montre que l'expression asymptotique de la durée de l'algorithme exhibe des fluctuations périodiques et par conséquent qu'il n'existe pas de distribution limite.
	www.inria.fr /rrrt/rr-3089.html (366 words)

	The quantum Mellin transform
		We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to 'hyperbolic phase space' (η, p
		We utilize this new transform to find quantum wavefunctions whose hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann–Zeta function.
		We finally give possible physical realizations to perform an indirect measurement of the hyperbolic momentum of a quantum system on the half-line.
	www.iop.org /EJ/abstract/1367-2630/8/12/328 (259 words)

	Digital Image Watermarking in the Wavelet Transform Domain
		Many image transforms have been considered, most prominent among them is the discrete cosine transform (DCT) which has also been favored in the early image and video coding standards.
		Other transforms that have been proposed for watermarking purposes include the discrete Fourier transform (DFT), the Fourier-Mellin transform and the fractal transform.
		The wavelet transform has a number of advantages over other transforms such as the DCT that can be exploited for both, image compression and watermarking applications.
	www.ganesh.org /publ/abstracts/2001/Meerwald01b.html (724 words)

	Boehmians
		Banerji and D. Loonker, On the Mellin transform of tempered Boehmians, Politehn.
		Karunakaran and N.V.Kalpakam, Hilbert Transform For Boehmians, Integral Transform.
		Karunakaran and N.V.Kalpakam, Boehmians and Fourier transforms, Integral Transform.
	www.math.ucf.edu /~piotr/boehmians.html (747 words)

	Centre for the Neural Basis of Hearing
		Our model for this process of size normalisation is based on the mathematics of scale invariance and it appears that the Mellin transform (MT), which represents this invariance, is quite directly applicable to what is going in in the human brain.
		The MT is an integral transform with the important property of invariance, within a phase factor, to dilations and contractions of the input signal:
		When this transform is applied to the 2-dimensional output of the earlier stages of AIM, a 2D 'Mellin Image' (MI) is created.
	www.mrc-cbu.cam.ac.uk /~tw01/cnbh/teaching/physics_project/mellin-phase-abstract.html (395 words)

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