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Construction theory of dyadic scale function and dyadic wavelet function
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作者 冉启文 冯英浚 孙学全 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2000年第4期25-27,共3页
We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the ... We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the construction of the dyadic wavelet and its necessary and sufficient condition. As an application, we also develop a pyramid algorithm of the dyadic wavelet decomposition. 展开更多
关键词 two SCALE INTEGRAL equation DYADIC wavelet function DYADIC SCALE function PYRAMID algorithm
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Customization of Wavelet Function for Pupil Fluctuation Analysis to Evaluate Levels of Sleepiness
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作者 Ruben-Dario Pinzon-Morales Yutaka Hirata 《通讯和计算机(中英文版)》 2013年第5期585-592,共8页
关键词 小波函数 波动分析 瞳孔 定制 DAUBECHIES小波 嗜睡 离散小波变换 评价
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Cylindrical Guided Wave Signals for Underground Pipe Inspection using Different Continuous Wavelet Mother Functions 被引量:1
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作者 Rais Ahmad Tribikram Kundu 《Journal of Civil Engineering and Architecture》 2011年第12期1103-1110,共8页
Over the past decade, wavelets provided a powerful and flexible set of tools for handling fundamental problems in science and engineering. Wavelet analyses are being used for solving problems in different engineering ... Over the past decade, wavelets provided a powerful and flexible set of tools for handling fundamental problems in science and engineering. Wavelet analyses are being used for solving problems in different engineering areas like audio de-noising, signal compression, object detection, image decomposition, speech recognition etc. Wavelet analysis employs orthonormal as well as non-orthonornal functions. This research investigates the effectiveness of wavelet analysis in detecting defects in underground steel pipe networks. Continuous Wavelet Transforms (CWT) has been performed on the received signals of cylindrical guided waves. Cylindrical Guided waves are generated and propagated through the pipe wall boundaries in a pitch-catch system. Piezo-electric transducers are used to generate as well as receive guided waves. Several mother wavelet functions such as Daubechies, Symlet, Coiflet and Meyer have been used for the Continuous Wavelet Transform to investigate the most suitable function for defect detection. This research also investigates the effect of surrounding soil on wavelet transforms for different mother wavelet functions. 展开更多
关键词 wavelet analysis guided waves mother wavelet functions continuous wavelet transform.
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Wavelet-Based Fractal Function Approximation 被引量:1
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作者 Zhang Hejei Tao Ran Zhou Siyong & Wang Yue(Department of Electronic Engineering, Beijing Institute of Technology, 100081, P. R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1999年第4期60-66,共7页
In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which th... In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression. 展开更多
关键词 B-SPLINE wavelet scaling function Fractal function APPROXIMATION Quadratic programming.
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Local Extrema of Periodic Function’s Wavelet Transform 被引量:3
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作者 FAN Qi-bin SONG Xiao-yan 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第6期949-952,共4页
The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wave... The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal' s instantaneous amplitude and period. 展开更多
关键词 extrema periodic function wavelet transform time-frequency analysis
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Phase spectrum estimation of the seismic wavelet based on a criterion function 被引量:4
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作者 Yu Yongcai Wang Shangxu +1 位作者 Yuan Sanyi Qi Pengfei 《Petroleum Science》 SCIE CAS CSCD 2012年第2期170-181,共12页
Phase spectrum estimation of the seismic wavelet is an important issue in high-resolution seismic data processing and interpretation. On the basis of two patterns of constant-phase rotation and root transform for wave... Phase spectrum estimation of the seismic wavelet is an important issue in high-resolution seismic data processing and interpretation. On the basis of two patterns of constant-phase rotation and root transform for wavelet phase spectrum variation, we introduce six sparse criteria, including Lu’s improved kurtosis criterion, the parsimony criterion, exponential transform criterion, Sech criterion, Cauchy criterion, and the modified Cauchy criterion, to phase spectrum estimation of the seismic wavelet, obtaining an equivalent effect to the kurtosis criterion. Through numerical experiments, we find that when the reflectivity is not a sparse sequence, the estimated phase spectrum of the seismic wavelet based on the criterion function will deviate from the true value. In order to eliminate the influence of non-sparse reflectivity series in a single trace, we apply the method to the multi-trace seismogram, improving the accuracy of seismic wavelet phase spectrum estimation. 展开更多
关键词 Seismic wavelet phase spectrum criterion function SPARSE
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Steganography based on wavelet transform and modulus function 被引量:1
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作者 Kang Zhiwei Liu Jing He Yigang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第3期628-632,共5页
In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a nove... In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image. 展开更多
关键词 STEGANOGRAPHY capacity wavelet transform modulus function HVS.
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Gaussian Functions,Γ-Functions and Wavelets 被引量:1
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作者 蔡涛 许天周 《Journal of Beijing Institute of Technology》 EI CAS 2003年第2期198-201,共4页
The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following th... The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following the train of thought in one dimensional situation, the relation between n dimensional Gaussian function and Γ function is given. By these, the possibility of arbitrary derivative of an n dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ function as well as in finding high dimensional mother wavelets. 展开更多
关键词 Gaussian function Γfunction wavelet
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Nonstationary Wavelets Related to the Walsh Functions 被引量:1
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作者 Yuri A. Farkov Evgeny A. Rodionov 《American Journal of Computational Mathematics》 2012年第2期82-87,共6页
Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of... Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of parameters. Application to compression of fractal functions are also discussed. 展开更多
关键词 WALSH functionS NONSTATIONARY DYADIC waveletS Fractal functionS Adapted MULTIRESOLUTION Analysis
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UNIFORM ANALYTIC CONSTRUCTION OF WAVELET ANALYSIS FILTERS BASED ON SINE AND COSINE TRIGONOMETRIC FUNCTIONS 被引量:1
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作者 李建平 唐远炎 +1 位作者 严中洪 张万萍 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期569-585,共17页
Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructio... Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition. 展开更多
关键词 wavelet analysis filter trigonometric functions analytic construction
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APPLICATION OF WAVELET THEORY IN RESEARCHON WEIGHT FUNCTION OF MESHLESS METHOD 被引量:1
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作者 张红 张选兵 葛修润 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第5期662-666,共5页
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is ort... Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given. 展开更多
关键词 meshless method weight function spline wavelet multiresolution analysis
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CHARACTERIZATIONS OF FUNDAMENTAL SCALING FUNCTIONS AND WAVELETS
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作者 Charles K.Chui 《Analysis in Theory and Applications》 1993年第3期37-52,共16页
The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.
关键词 CHARACTERIZATIONS OF FUNDAMENTAL SCALING functionS AND waveletS MALLAT
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Inversion of receiver function by wavelet transformation
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作者 吴庆举 田小波 +2 位作者 张乃铃 李桂银 曾融生 《Acta Seismologica Sinica(English Edition)》 CSCD 2003年第6期616-623,共8页
A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initi... A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution. 展开更多
关键词 receiver function wavelet transformation waveform inversion
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THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION
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作者 刘海峰 周炜星 +2 位作者 王辅臣 龚欣 于遵宏 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第9期1062-1070,共9页
Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spect... Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function. 展开更多
关键词 wavelet transform periodic function nonstationary periodic function Fourier transform
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THREE-DIMENSIONAL ANALYSIS OF FUNCTIONALLY GRADED PLATE BASED ON THE HAAR WAVELET METHOD 被引量:2
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作者 Zhang Chun Zhong Zheng 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第2期95-102,共8页
A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. Wit... A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied. 展开更多
关键词 functionally graded material rectangular plate Haar wavelet three-dimensional analysis
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Wavelet function estimation involving time series 被引量:1
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作者 Yuan Li Zhongjie Xie 《Chinese Science Bulletin》 SCIE EI CAS 1998年第7期553-556,共4页
Nonparametric regression models are considered. The nonparametric estimators for a regression function are given by wavelets. It is shown that under certain conditions, the wavelet estimators attain the optimal or nea... Nonparametric regression models are considered. The nonparametric estimators for a regression function are given by wavelets. It is shown that under certain conditions, the wavelet estimators attain the optimal or nearly optimal convergence rate in a ball of Besov spaces. 展开更多
关键词 regression function ESTIMATORS wavelets.
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Face Recognition Based on Wavelet Packet Coefficients and Radial Basis Function Neural Networks
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作者 Thangairulappan Kathirvalavakumar Jeyasingh Jebakumari Beulah Vasanthi 《Journal of Intelligent Learning Systems and Applications》 2013年第2期115-122,共8页
An efficient face recognition system with face image representation using averaged wavelet packet coefficients, compact and meaningful feature vectors dimensional reduction and recognition using radial basis function ... An efficient face recognition system with face image representation using averaged wavelet packet coefficients, compact and meaningful feature vectors dimensional reduction and recognition using radial basis function (RBF) neural network is presented. The face images are decomposed by 2-level two-dimensional (2-D) wavelet packet transformation. The wavelet packet coefficients obtained from the wavelet packet transformation are averaged using two different proposed methods. In the first method, wavelet packet coefficients of individual samples of a class are averaged then decomposed. The wavelet packet coefficients of all the samples of a class are averaged in the second method. The averaged wavelet packet coefficients are recognized by a RBF network. The proposed work tested on three face databases such as Olivetti-Oracle Research Lab (ORL), Japanese Female Facial Expression (JAFFE) and Essexface database. The proposed methods result in dimensionality reduction, low computational complexity and provide better recognition rates. The computational complexity is low as the dimensionality of the input pattern is reduced. 展开更多
关键词 Feature Extraction FACE Recognition wavelet PACKETS RADIAL BASIS function Neural Network
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基于小波核极限学习机的烟叶烘烤过程的智能识别
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作者 邢玉清 樊彩霞 +2 位作者 豆根生 宋朝鹏 吴莉莉 《中国烟草学报》 CAS CSCD 北大核心 2024年第1期55-62,共8页
烟叶烘烤设备操作复杂、技术含量高、熟练掌握烟叶烘烤技术人员不足等问题,影响了烟叶的烘烤质量。针对上述问题,本文提出了基于小波核极限学习机的烟叶烘烤过程的智能识别方法。实验中对三段式烘烤过程中的叶片变软、主脉变软、勾尖卷... 烟叶烘烤设备操作复杂、技术含量高、熟练掌握烟叶烘烤技术人员不足等问题,影响了烟叶的烘烤质量。针对上述问题,本文提出了基于小波核极限学习机的烟叶烘烤过程的智能识别方法。实验中对三段式烘烤过程中的叶片变软、主脉变软、勾尖卷边、小打筒、大打筒和干筋6个烘烤阶段分别提取了颜色、纹理和温湿度特征,组建了9维特征向量进入小波核极限学习机,通过增量型算法自适应地选择神经元个数,快速准确地识别了6个阶段,得到了98.33%的识别率。实验结果表明本文提出的基于小波核极限学习机的烟叶烘烤过程的智能识别方法具有一定的可行性,为研发烟叶烘烤智能调控系统奠定了理论基础。 展开更多
关键词 极限学习机 小波核函数 烟叶烘烤 特征提取 识别
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Predicting Wavelet-Transformed Stock Prices Using a Vanishing Gradient Resilient Optimized Gated Recurrent Unit with a Time Lag
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作者 Luyandza Sindi Mamba Antony Ngunyi Lawrence Nderu 《Journal of Data Analysis and Information Processing》 2023年第1期49-68,共20页
The development of accurate prediction models continues to be highly beneficial in myriad disciplines. Deep learning models have performed well in stock price prediction and give high accuracy. However, these models a... The development of accurate prediction models continues to be highly beneficial in myriad disciplines. Deep learning models have performed well in stock price prediction and give high accuracy. However, these models are largely affected by the vanishing gradient problem escalated by some activation functions. This study proposes the use of the Vanishing Gradient Resilient Optimized Gated Recurrent Unit (OGRU) model with a scaled mean Approximation Coefficient (AC) time lag which should counter slow convergence, vanishing gradient and large error metrics. This study employed the Rectified Linear Unit (ReLU), Hyperbolic Tangent (Tanh), Sigmoid and Exponential Linear Unit (ELU) activation functions. Real-life datasets including the daily Apple and 5-minute Netflix closing stock prices were used, and they were decomposed using the Stationary Wavelet Transform (SWT). The decomposed series formed a decomposed data model which was compared to an undecomposed data model with similar hyperparameters and different default lags. The Apple daily dataset performed well with a Default_1 lag, using an undecomposed data model and the ReLU, attaining 0.01312, 0.00854 and 3.67 minutes for RMSE, MAE and runtime. The Netflix data performed best with the MeanAC_42 lag, using decomposed data model and the ELU achieving 0.00620, 0.00487 and 3.01 minutes for the same metrics. 展开更多
关键词 Optimized Gated Recurrent Unit Approximation Coefficient Stationary wavelet Transform Activation function Time Lag
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均匀磁场下二维拓扑绝缘体边缘态的多重Andreev反射研究
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作者 杨雪 吕博 《现代电子技术》 北大核心 2024年第4期17-22,共6页
研究均匀磁场下的二维拓扑绝缘体在超导隧道结中的电压偏置约瑟夫森结的输运性质,电流-电压特性显示了马约拉纳束缚态的存在。在亚谐隙结构中,也可以观察到磁场对超导能隙的影响。研究结果表明,在S波超导体/正常金属/S波超导结的隧道谱... 研究均匀磁场下的二维拓扑绝缘体在超导隧道结中的电压偏置约瑟夫森结的输运性质,电流-电压特性显示了马约拉纳束缚态的存在。在亚谐隙结构中,也可以观察到磁场对超导能隙的影响。研究结果表明,在S波超导体/正常金属/S波超导结的隧道谱中存在亚谐隙结构。透明度只影响超导结的零偏压电导值的大小,而不影响亚谐隙结构的位置。但是在磁场作用下,亚谐隙结构会发生变化,不再固定出现在特定位置。这一结果对应于拓扑螺旋态中超导和铁磁序之间的相互作用。 展开更多
关键词 拓扑绝缘体 多重Andreev反射 超导隧道结 约瑟夫森结 亚谐隙结构 马约拉纳束缚态 S波超导体 准粒子波函数
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