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Rice Crop Digital Image Compression Technology Based on Discrete fourier transform

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Agricultural Science & Technology 2012年第3期13卷 634-637页

作者：黄新民姚军财何军锋申静黄晓洲陕西理工学院科技处陕西汉中723000 陕西理工学院物理与电信工程学院陕西汉中723000 陕西理工学院数学与计算机科学学院陕西汉中723000 陕西理工学院教育科学学院陕西汉中723000

[Objective] To study the digital image compression technology in rice monitoring system. [Method] A digital image compression technology program based on the discrete fourier transform was proposed, and simulation experiments were carried out to compress the image at different compression ratios. [Result] When com- pression ratios were less than 30, the compression ratio, image entropy, average codeword length, coding efficiency and redundancy which reflected the quality of the coding, and the parameter PSNR which estimated the fidelity of the compressed im- age were all achieved good results that human eye could barely percept the differ- ence between the original image and decompressed image; and when the compres- sion ratios were more than 30, there was a certain distortion in the decompressed image. And when the compression ratio was 91.516 3, although the image had some distortion, the PSNR was still achieved to 21.528 2, and human eye could accept the decompressed image intuitively within the acceptable error range. [Conclusion] The results show that the proposed image compression program is a viable, effective, and better image compression technology which can satisfy the requirements of the crop monitoring system on image storage, transforming and transporting.

关键词： Digital image Compression fourier transform Peak Signal-to-Noise Ratio

A property of Pisot numbers and fourier transforms of self-similar measures

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Science China Mathematics 2012年第8期55卷 1721-1733页

作者： HU Tian-You Department of Mathematics University of Wisconsin-Green Bay Wisconsin WI 54311 USA

For any Pisot number β it is known that the set F（β） ={t ： limn→∞‖tβn‖ = 0} is countable, where ‖α‖ is the distance between a real number a and the set of integers. In this paper it is proved that every member in this set is of the form cβn, where n is a nonnegative integer and e is determined by a linear system of equations. Furthermore, for some self-similar measures μ associated with β, the limit at infinity of the fourier transforms limn→μ（tβn）≠0 if and only if t is in a certain subset of F（β）. This generalizes a similar result of Huang and Strichartz.

关键词： Bernoulli convolution fourier transform minimal polynomial Pisot number recurrence relation,self-similar measure

High order generalized permutational fractional fourier transforms

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Chinese Physics B 2004年第2期13卷 178-186页

作者：冉启文袁琳谭立英马晶王骐 DepartmentofMathematics HarbinInstituteofTechnologyHarbin150001China StateKeyLaboratoryofTunableLaserTechnology ResearchInstituteofOptlc-ElectronicsHarbinInstituteofTechnologyHarbin150001China

We generalize the definition of the fractional fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional fourier transform (HGPFRFT),is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +∞,M = 4k (k is a natural number), and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.

关键词： fourier transform fractional fourier transform permutational fractional fourier transform

Detection of surface cutting defect on magnet using fourier image reconstruction

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Journal of Central South University 2016年第5期23卷 1123-1131页

作者：王福亮左博 School of Mechanical and Electrical Engineering Central South University State Key Laboratory of High Performance Complex Manufacturing (Central South University)

A magnet is an important component of a speaker,as it makes the coil move back forth,and it is commonly used in mobile information *** may appear on the surface of the magnet while cutting it into smaller slices,and hence,automatic detection of surface cutting defect detection becomes an important task for magnet *** this work,an image-based detection system for magnet surface defect was constructed,a fourier image reconstruction based on the magnet surface image processing method was *** fourier transform was used to get the spectrum image of the magnet image,and the defect was shown as a bright line in *** Hough transform was used to detect the angle of the bright line,and this line was removed to eliminate the defect from the original gray image;then the inverse fourier transform was applied to get the background gray *** defect region was obtained by evaluating the gray-level differences between the original image and the background gray ***,the effects of several parameters in this method were studied and the optimized values were *** results show that the proposed method can detect surface cutting defects in a magnet automatically and efficiently.

关键词： defect detection image process magnet fourier transform

fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

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Applied Mathematics and Mechanics(English Edition) 2009年第9期30卷 1177-1182页

作者：尚月强何银年 Faculty of Science Xi'an Jiaotong University School of Mathematics and Computer Science Guizhou Normal University

Schwarz methods are an important type of domain decomposition methods. Using the fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.

关键词： domain decomposition algorithm Schwarz method fourier transform biharmonic equation

An application of Chen's theorem to convergence of fourier multiplier transforms

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Applied Mathematics(A Journal of Chinese Universities) 2013年第4期28卷 455-464页

作者： SHI Xian-liang CHEN Yang HU Lan College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University

Let V be a star shaped region. In 2006, Colzani, Meaney and Prestini proved that if function f satisfies some condition, then the multiplier transform with the characteristic function of tV as the multiplier tends to f almost everywhere, when t goes to∞. In this paper we use a Theorem established by *** to show that if we change their multiplier, then the condition on f can be weakened.

关键词： fourier transform multiplier summability convergence almost everywhere

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Journal of Beijing Institute of Technology 1995年第2期4卷 105+99-105页

作者：祝同江北京理工大学应用数学系

Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their fourier transformation.

关键词： fourier transform generalized functions/similarity transformation regularizing functionals

Classical fourier Analysis over Homogeneous Spaces of Compact Groups

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Analysis in Theory and Applications 2016年第4期32卷 339-354页

作者： Arash Ghaani Farashahi Numerical Harmonic Analysis Group (NuHAG) Faculty Mathematics University of Vienna

This paper introduces a unified operator theory approach to the abstract fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of fourier analysis for the Hilbert function space L^2 （G / H, μ）.

关键词： Compact group homogeneous space dual space fourier transform Plancherel(trace) formula Peter-Weyl Theorem

Efficient Option Pricing Methods Based on fourier Series Expansions

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Journal of Mathematical Research and Exposition 2011年第1期31卷 12-22页

作者： Sio Chong U Department of Mathematics University of Macao

A novel option pricing method based on fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on fourier, fourier-cosine and fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L^vy models are also given to compare these new methods with the Fang and Oosterlee＇s method and other methods.

关键词： option pricing Levy process fourier transform fourier expansions.