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1.
The Two-Dimensional Clifford-Fourier Transform 总被引:1,自引:0,他引:1
Fred Brackx Nele De Schepper Frank Sommen 《Journal of Mathematical Imaging and Vision》2006,26(1-2):5-18
Recently several generalizations to higher dimension of the Fourier transform using Clifford algebra have been introduced,
including the Clifford-Fourier transform by the authors, defined as an operator exponential with a Clifford algebra-valued
kernel.
In this paper an overview is given of all these generalizations and an in depth study of the two-dimensional Clifford-Fourier
transform of the authors is presented. In this special two-dimensional case a closed form for the integral kernel may be obtained,
leading to further properties, both in the L
1 and in the L
2 context. Furthermore, based on this Clifford-Fourier transform Clifford-Gabor filters are introduced.
AMS subject classification numbers: 42B10, 30G35
Fred Brackx received a diploma degree in mathematics from Ghent University, Belgium, in 1970 and a Ph.D. degree in mathematics from the
same university in 1973. Since 1984 he is professor for mathematical analysis at Ghent University and currently he is leading
the Clifford Research Group. His main interests are function theory and functional analysis for functions with values in quaternion
and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal
polynomials and multi-dimensional wavelets.
Nele De Schepper received a diploma degree in mathematics from Ghent University, Belgium, in 2001. Since then she holds an assistantship at
the Department of Mathematical Analysis of Ghent University and is a member of the Clifford Research Group. Her main interests
are function theory and functional analysis for functions with values in Clifford algebras. The research covers generalized
Fourier transforms, orthogonal polynomials and multi-dimensional wavelets.
Frank Sommen received a diploma degree in mathematics from Ghent University, Belgium, in 1978, a Ph.D. degree in mathematics from the
same university in 1980, and a habilitation degree in mathematical analysis in 1984. From 1978 until 1999 he was at the National
Fund for Scientific Research (Flanders). Since 2000 he holds a Research professorship at Ghent University. His main interests
are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers
Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets,
algebraic analysis, hyperfunctions and radial algebra. 相似文献
2.
Javier Ramírez Antonio García Uwe Meyer-Bäse Fred Taylor Antonio Lloris 《The Journal of VLSI Signal Processing》2003,33(1-2):171-190
Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength). 相似文献
3.
A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained. 相似文献
4.
5.
6.
S. K. Chen A. Serquis G. Serrano K. A. Yates M. G. Blamire D. Guthrie J. Cooper H. Wang S. Margadonna J. L. MacManus‐Driscoll 《Advanced functional materials》2008,18(1):113-120
By applying a combination of characterisation tools, changes in structural and superconducting properties with nominal Mg non‐stoichiometry in MgxB2 are found. The non‐stoichiometry produces enhanced in‐field critical current densities (Jc's) and upper critical field / irreversibility field (Hc2/Hirr(T)) values. Upper critical fields of ~ 21 T (4.2 K) were obtained in nominal Mg‐deficient samples compared to ~ 17 T (4.2 K) for near‐stoichiometric samples. 相似文献
7.
Yoon Carolyn; Feinberg Fred; Hu Ping; Gutchess Angela Hall; Hedden Trey; Chen Hiu-Ying Mary; Jing Qicheng; Cui Yao; Park Denise C. 《Canadian Metallurgical Quarterly》2004,19(3):379
Understanding how aging influences cognition across different cultures has been hindered by a lack of standardized, cross-referenced verbal stimuli. This study introduces a database of such item-level stimuli for both younger and older adults, in China and the United States, and makes 3 distinct contributions. First, the authors specify which item categories generalize across age and/or cultural groups, rigorously quantifying differences among them. Second, they introduce novel, powerful methods to measure between-group differences in freely generated ranked data, the rank-ordered logit model and Hellinger Affinity. Finally, a broad archive of tested, cross-linguistic stimuli is now freely available to researchers: data, similarity measures, and all stimulus materials for 105 categories and 4 culture-by-age groups, comprising over 10,000 fully translated unique item responses. (PsycINFO Database Record (c) 2010 APA, all rights reserved) 相似文献
8.
9.
The long‐term consequences of the sale of public sector dwellings to sitting tenants are under‐researched; in particular, the experience of tenant purchasers in the housing market subsequent to purchase is little known. This paper reports research designed to fill this gap in knowledge. Over 200 tenants who had bought their dwelling from the Scottish Special Housing Association and subsequently resold on the open market were traced using the Register fo Sasines and the Land Register and interviewed. Most had made considerable capital gains on resale and had used some of the realised capital to trade up in the housing market. They were, on average, slightly more affluent and younger than sitting tenant purchasers generally; they represented a group of households who were privileged within the public sector through living as tenants in the best stock and who were enabled by the Right to Buy to convert that good luck into hard cash and move into mainstream owner occupation. This good luck compounded the advantaged position vis‐à‐vis other tenants that they enjoyed in the labour market. 相似文献
10.
Nils Hallbäck Fred Nilsson 《Fatigue & Fracture of Engineering Materials & Structures》1992,15(2):173-185
The fracture assessment of structures subjected to secondary loading systems was studied by FEM-analysis of a few illustrative two-dimensional examples. The first example is an edge-cracked plate with a thermal gradient. The FEM-calculations revealed that a purely elastic analysis yielded J-values that are in most cases considerably more conservative than the ones calculated from an elastic-plastic analysis. The results were further compared with different engineering type non-linear estimates. As a second example a crack emanating from a semi-circular notch in a rectangular plate was chosen. The plate was subjected to uniaxial tension along its boundaries. It turned out that for the cases considered the J-values were fairly close to those elastically predicted. 相似文献