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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.
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
5.
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
6.
A meta-analysis of 47 studies was used to shed light on inconsistencies in the concurrent association between parental caregiving and child externalizing behavior. Parent–child associations were strongest when the measure of caregiving relied on observations or interviews, as opposed to questionnaires, and when the measure tapped combinations of parent behaviors (patterns), as opposed to single behaviors. Stronger parent–child associations were also found for older than for younger children, and for mothers than for fathers. Finally, externalizing was more strongly linked to parental caregiving for boys than for girls, especially among preadolescents and their mothers. The meta-analysis helps account for inconsistencies in findings across previous studies and supports theories emphasizing reciprocity of parent and child behavior. (PsycINFO Database Record (c) 2010 APA, all rights reserved) 相似文献
7.
Faking behavior was studied by comparing the personality profiles of 161 job applicants (motivated to be hired) with those of a control group of 73 graduate and undergraduate business students (motivated to obtain personal information for their own enlightenment). 44% of the Ss were female. Both groups were instructed to describe themselves honestly while completing the Self-Perception Test. Applicants did "fake good," scoring significantly higher on 10 of 11 scales; variance was significantly lower among applicants on 7 scales. Gender differences, consistent with cultural stereotypes, occurred on 5 scales. Overall profile shapes were virtually identical for student and applicant groups, suggesting that faking may not have dramatically altered the essence of the personality constructs. The scales of the test were found to have high reliability. Scale independence is discussed in relation to the 5-factor model of personality. (PsycINFO Database Record (c) 2010 APA, all rights reserved) 相似文献
8.
Various aspects on probabilistic modelling of cleavage fracture are discussed. The investigation involves consideration of
a unit cell with an explicitly modelled void. The results from this model are compared with results for the case when the
void content is accounted for in the sense of a Gurson-Tvergaard law. It is found that explicit modelling of the void can
give substantially different results for the fracture probability. The effect depends on the exponent in the assumed Weibull
distribution, the threshold stress, the constraint conditions and the hardening of the material.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
9.
10.
Intelligent scheduling with tabu search: An application to jobs with linear delay penalties and sequence-dependent setup costs and times 总被引:3,自引:0,他引:3
In this article we study thetabu search (TS) method in an application for solving an important class of scheduling problems. Tabu search is characterized by integrating artificial intelligence and optimization principles, with particular emphasis on exploiting flexible memory structures, to yield a highly effective solution procedure. We first discuss the problem of minimizing the sum of the setup costs and linear delay penalties when N jobs, arriving at time zero, are to be scheduled for sequential processing on a continuously available machine. A prototype TS method is developed for this problem using the common approach of exchanging the position of two jobs to transform one schedule into another. A more powerful method is then developed that employs insert moves in combination with swap moves to search the solution space. This method and the best parameters found for it during the preliminary experimentation with the prototype procedure are used to obtain solutions to a more complex problem that considers setup times in addition to setup costs. In this case, our procedure succeeded in finding optimal solutions to all problems for which these solutions are known and a better solution to a larger problem for which optimizing procedures exceeded a specified time limit (branch and bound) or reached a memory overflow (branch and bound/dynamic programming) before normal termination. These experiments confirm not only the effectiveness but also the robustness of the TS method, in terms of the solution quality obtained with a common set of parameter choices for two related but different problems. 相似文献