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Fractal Surface Synthesis Based on Two Dimensional discrete fourier transform

Chinese Journal of Mechanical Engineering 2013年第6期26卷 1101-1108页

作者： ZHOU Chao GAO Chenghui HUANG Jianmeng School of Mechanical Engineering and Automation Fuzhou University Fujian Provincial Research Center of Digital Design for Manufacturing

The discrete fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.

关键词： fractional Brownian motion discrete fourier transform fractal surface power spectrum

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Theory and algorithms for two-dimensional warped discrete fourier transform

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控制理论与应用（英文版） 2006年第3期4卷 281-285页

作者： Xichun ZHANG Gang WEI School of Electronics ＆ Information Engineering South China University of Technology Guangzhou Guangdong 510640 China

In this paper, the two-dimensional Warped discrete fourier transform （2-D WDFT） is developed based on the concept of the 1-D WDFT. An exact computation algorithm is developed for 2-D WDFT based on matrix factorizing with special structure. A fast algorithm is then proposed to reduce greatly the computational complexity of the inverse 2-D WDFT. Finally, numerical examples are given to show the efficiency of the proposed approach.

关键词： discrete fourier transform Non-uniform DFT Warped DFT

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Design of a Multifrequency Signal Parameter Estimation Method for the Distribution Network Based on HIpST

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Energy Engineering 2024年第3期121卷 729-746页

作者： Bin Liu Shuai Liang Renjie Ding Shuguang Li Tongliao Power Supply Company State Grid East Inner Mongolia Electric Power Co.Ltd.Tongliao028000China School of Electrical Engineering Northeast Electric Power UniversityJilin132012China

The application of traditional synchronous measurement methods is limited by frequent fluctuations of electrical signals and complex frequency components in distribution ***,it is critical to find solutions to the issues of multifrequency parameter estimation and synchronous measurement estimation accuracy in the complex environment of distribution *** utilizing the multifrequency sensing capabilities of discrete fourier transform signals and Taylor series for dynamic signal processing,a multifrequency signal estimation approach based on HT-IpDFT-STWLS(HIpST)for distribution networks is ***,by introducing the Hilbert transform(HT),the influence of noise on the estimation algorithm is ***,signal frequency components are obtained on the basis of the calculated signal envelope spectrum,and the interpolated discrete fourier transform(IpDFT)frequency coarse estimation results are used as the initial values of symmetric Taylor weighted least squares(STWLS)to achieve high-precision parameter estimation under the dynamic changes of the signal,and the method increases the number of discrete ***,the accuracy of this proposed method is verified by simulation *** show that this proposed method can accurately achieve the parameter estimation of multifrequency signals in distribution *** approach provides a solution for the application of phasor measurement units in distribution networks.

关键词： discrete fourier transform taylor series hilbert transform multifrequency signal parameter estimation

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Seismic dynamic stability of double-slider rock slopes containing tension cracks

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山地科学学报(英文) 2023年第7期20卷 2093-2106页

作者： ZHU Chen-hao ZHAO Lian-heng HU Shi-hong ZUO Shi YU Cheng-hao School of Civil Engineering Central South UniversityChangsha 410075China Key Laboratory of Heavy-haul Railway Engineering Structure Ministry of EducationCentral South UniversityChangsha 410075China

Earthquakes have significant impact on rock slopes,thus studying the seismic stability of double-slider rock slopes containing tension cracks is *** proposed an analysis method on the seismic dynamic slope *** method utilizes discrete fourier transform to decompose real earthquake waves into a combination of harmonic *** waves are then used in conjunction with the pseudo-dynamic method and safety factor calculation formula to compute the safety *** approach accurately captures the influence of seismic time history characteristics on the dynamic stability of double-slider rock slopes containing tension *** minimum safety factor in the obtained time history curves of the safety factor reflects the most unfavorable state of the slopes under seismic *** analysis is conducted using six sets of actual earthquake ground motion data obtained from the Pacific Earthquake Engineering Research Center’s NGAWest2 ground-shaking record *** conclusions are as follows:(1)There is an inverse correlation between the average seismic acceleration amplitude and the minimum safety ***,the seismic acceleration amplitude standard deviation shows a positive correlation with the minimum safety *** global sensitivity of geometric parameters in the slope model is higher than other influencing factors.(2)The proposed dynamic stability analysis method can capture the dynamic characteristics of earthquakes,emphasizing the minimum safety factor of the slope in the seismic time history as a stability *** contrast,the pseudo-static method may yield unsafe results.(3)A safety factor expression considering hydrostatic pressure is proposed.A negative correlation was observed between the height of the water level line and the minimum safety factor.

关键词： Earthquake Rock slope Tension crack Modified Pseudo-Dynamic Method discrete fourier transform

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PM-DFT:A New Local Invariant Descriptor Towards Image Copy Detection

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Journal of Computer Science & Technology 2011年第3期26卷 558-566,F0003页

作者：凌贺飞王丽云严灵毓邹复好卢正鼎 School of Computer Science and Technology Huazhong University of Science and Technology

Currently, global-features-based image copy detection is vulnerable to geometric transformations like cropping, shift, and rotations. To resolve this problem, some algorithms based on local descriptors have been proposed. However, the local descriptors, which were originally designed for object recognition, are not suitable for copy detection because they cause the problems of false positives and ambiguities. Instead of relying on the local gradient statistic as many existing descriptors do, we propose a new invariant local descriptor based on local polar-mapping and discrete fourier transform. Then based on this descriptor, we propose a new framework of copy detection, in which virtual prior attacks and attack weight are employed for training and selecting only a few robust features. This consequently improves the storage and detection efficiency. In addition, it is worth noting that the feature matching takes the locations and orientations of interest points into consideration, which increases the number of matched regions and improves the recall. Experimental results show that the new descriptor is more robust and distinctive, and the proposed copy detection scheme using this descriptor can substantially enhance the accuracy and recall of copy detection and lower the false positives and ambiguities.

关键词： copy detection local invariant descriptor discrete fourier transform polar-mapping

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Windowing Techniques, the Welch Method for Improvement of Power Spectrum Estimation

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Computers, Materials & Continua 2021年第6期67卷 3983-4003页

作者： Dah-Jing Jwo Wei-Yeh Chang I-Hua Wu Department of Communications Navigation and Control EngineeringTaiwan Ocean UniversityKeelung202-24TaiwanChina Innovative Navigation Technology Ltd. Kaohsiung801TaiwanChina

This paper revisits the characteristics of windowing techniques with various window functions involved,and successively investigates spectral leakage mitigation utilizing the Welch *** discrete fourier transform(DFT)is ubiquitous in digital signal processing(DSP)for the spectrum analysis and can be efciently realized by the fast fourier transform(FFT).The sampling signal will result in distortion and thus may cause unpredictable spectral leakage in discrete spectrum when the DFT is *** is implemented by multiplying the input signal with a window function and windowing amplitude modulates the input signal so that the spectral leakage is evened ***,windowing processing reduces the amplitude of the samples at the beginning and end of the *** addition to selecting appropriate window functions,a pretreatment method,such as the Welch method,is effective to mitigate the spectral *** to the noise caused by imperfect,nite data,the noise reduction from Welch’s method is a desired *** nonparametric Welch method is an improvement on the periodogram spectrum estimation method where the signal-to-noise ratio(SNR)is high and mitigates noise in the estimated power spectra in exchange for frequency resolution *** periodogram technique based on Welch method is capable of providing good resolution if data length samples are appropriately *** design of nite impulse response(FIR)digital lter using the window technique is rstly *** inuence of various window functions on the fourier transform spectrum of the signals is *** on spectral resolution based on the traditional power spectrum estimation and various window-function-based Welch power spectrum estimations is presented.

关键词： Window functions Welch method discrete fourier transform spectral leakage

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Two-Dimensional Interpolation Criterion Using DFT Coefficients

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Computers, Materials & Continua 2020年第2期62卷 849-859页

作者： Yuan Chen Liangtao Duan Weize Sun Jingxin Xu University of Science&Technology Beijing BeijingChina ShenZhen University ShenzhenChina Department of Housing and Public Works Queensland GovernmentBrisbaneAustralia

In this paper,we address the frequency estimator for 2-dimensional(2-D)complex sinusoids in the presence of white Gaussian *** the use of the sinc function model of the discrete fourier transform(DFT)coefficients on the input data,a fast and accurate frequency estimator is devised,where only the DFT coefficient with the highest magnitude and its four neighbors are *** analysis is also included to investigate the accuracy of the proposed *** results are conducted to demonstrate the superiority of the developed scheme,in terms of the estimation performance and computational complexity.

关键词： 2-D Frequency estimation parameter estimation interpolation discrete fourier transform

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The Impact of Agricultural Practices in China on Land-Atmosphere Interactions

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Advances in Atmospheric Sciences 2011年第4期28卷 821-831页

作者：徐兴奎 Jason K.LEVY State Key Laboratory of Earth Surface Processes and Resource Ecology Beijing Normal University Institute of Atmospheric Physics Chinese Academy of Science L.Douglas Wilder School of Government and Public Affairs Virginia Commonwealth University Richmond

Human-induced land use changes and the resulting alterations in vegetation features are major but poorly recognized drivers of regional climatic *** order to investigate the impacts of anthropogenically-induced seasonal vegetation cover changes on regional climate in China,harmonic analysis is applied to 1982-2000 National Oceanic and Atmospheric Administration（NOAA） Advanced Very High Resolution Radiometer（AVVHRR）-derived normalized difference vegetation index（NDVI） time series（ten day interval data）.For two climatic divisions of South China,it is shown that the first harmonic term is in phase with air temperature,while the second and third harmonics are in phase with agricultural *** Penman-Monteith Equation and the Complementary Relationship Areal Evapotranspiration（CRAE） model suggest that monthly mean evapotranspiration is out of phase with temperature and precipitation in regions with signiffcant second or third ***,seasonal vegetation cover changes associated with agricultural cultivation are identiffed：for cropped areas,the temperature and precipitation time series have a single maximum value,while the monthly evapotranspiration time series has a bimodal *** is hypothesized that multi-cropping causes the land surface albedo to sharply increase during harvesting,thereby altering the energy distribution ratio and contributing to observed seasonal vegetation cover changes.

关键词： NDVI land surface cover phenologies multi-crop latent heat discrete fourier transform

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OUTPUT MAXIMIZATION CONTROL FOR VSCF WIND ENERGY CONVERSION SYSTEM USING EXTREMUM CONTROL STRATEGY

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Transactions of Nanjing University of Aeronautics and Astronautics 2013年第2期30卷 185-192页

作者：付大丰马运东 College of Automation Engineering Nanjing University of Aeronautics and Astronautics

The energy conversion optimization control strategy is presented for a family of horizontal-axis variablespeed fixed-pitch wind energy conversion systems,working in the partial load *** system uses a variablespeed wind turbine(VSWT)driving a squirrel-cage induction generator(SCIG)connected to a grid.A new maximum power point tracking(MPPT)approach is proposed based on the extremum seeking control principles under the assumption that the wind turbine model and its parameters are poorly *** aim is to drive the average position of the operation point close to *** the wind turbulence is used as search disturbance instead of inducing new sinusoidal search *** discrete fourier transform(DFT)process of some available measures estimates the distance of operation point to *** effectiveness of the proposed MPPT approach is validated under different operation conditions by numerical simulations in MATLAB/*** simulation results prove that the new approach can effectively suppress the vibration of system and enhance the dynamic performance of system.

关键词： wind energy conversion systems maximum power point tracking extremum control strategy discrete fourier transform

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BIVARIATE REAL-VALUED ORTHOGONAL PERIODIC WAVELETS

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Analysis in Theory and Applications 2005年第3期21卷 266-279页

作者： Qiang Li Xuezhang Liang Institute of Mathematics Jilin University Changchun 130012 P. R. China

In this paper, we construct a kind of bivariate real-valued orthogonal periodic wavelets. The corre-sponding decomposition and reconstruction algorithms involve only 8 terms respectively which are very simple in pract... 详细信息

关键词： periodic multiresolution analysis two-scale dilation equation periodic wavelet discrete fourier transform

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