The Construction of a Class of Compactly Supported Orthogonal Matrix-valued

In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.

A CLASS OF COMPACTLY SUPPORTED ORTHOGONAL SYMMETRIC COMPLEX WAVELETS WITH DILATION FACTOR 3

When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex that illustrate the corresponding results. wavelets. In the end, there are several examples

Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets

The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.

On the Zeros of Daubechies Orthogonal and Biorthogonal Wavelets

In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogonal Daubechies families of wavelets are considered and their filters are derived. In particular, the Biorthogonal wavelets Bior3.5, Bior3.9 and Bior6.8 are examined and the zeros distribution of their polynomials associated filters are located. We also examine the locations of these zeros of the filters associated with the two orthogonal wavelets db6 and db8.

The Algorithm of Balanced Orthogonal Multiwavelets and Its Application in Denoising

In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness, a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed. Multiwavelets have several scaling functions and wavelet functions, and possess excellent properties that a scalar wavelet cannot satisfy simultaneously, and match the different characteristics of signals. Moreover, the balanced orthogonal multiwavelets can avoid the Gibbs phenomena and their processes have the advantages in denoising. Therefore, the denoising based on the algorithm of balanced orthogonal multiwavelets is introduced into the signal process. The algorithm of bal- anced orthogonal multiwavelet and the implementation steps of this denoising are described. The experimental compar- ison of the denoising effect between this algorithm and the traditional multiwavelet algorithm was done. The experi- ments indieate that this method is effective and feasible to extract the fault feature submerged in heavy noise.

Real-time Extraction of Target Position Information Based on Bi-orthogonal Wavelets

Extraction of flying target position information is the prerequisite for passive infrared guided missiles to track the target. The existing missile detection system senses the target's infrared radiation, and then the generated signal is sent to signal processing circuits for extracting the target position information. In order to improve anti-interference capacity of the detection system, an algorithm of module maximum edge detection based on the bi-orthogonal wavelets is proposed to replace its hardware. The signal can be decomposed in one layer, only its high frequency detail is reconstructed. After some calculations, the average target position can be obtained. The algorithm's real-time implementation with DSP is also discussed. To reduce the execution time, the program structure can be optimized with double buffers in memory. This implementation is verified by simulations. The results show that the method has only a small amount of calculations, can meet the requirements for finding out the target position in real-time and needs not the traditional processing circuit.

An Orthogonal Wavelet Transform Fractionally Spaced Blind Equalization Algorithm Based on the Optimization of Genetic Algorithm

An orthogonal wavelet transform fractionally spaced blind equalization algorithm based on the optimization of genetic algorithm(WTFSE-GA) is proposed in viewof the lowconvergence rate,large steady-state mean square error and local convergence of traditional constant modulus blind equalization algorithm(CMA).The proposed algorithm can reduce the signal autocorrelation through the orthogonal wavelet transform of input signal of fractionally spaced blind equalizer,and decrease the possibility of CMA local convergence by using the global random search characteristics of genetic algorithm to optimize the equalizer weight vector.The proposed algorithm has the faster convergence rate and smaller mean square error compared with FSE and WT-FSE.The efficiency of the proposed algorithm is proved by computer simulation of underwater acoustic channels.

THE CONSTRUCTION OF ORTHOGONAL WAVELET BASIS ON[0,1] AND NUMERICAL SIMULATION

In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet ba-sis and differential operator, which affects on the basis, to functions belonging to L2 [0, 1 ]. Numerical computation indicate the stability and effectiveness of the algorithm.

Characterizations of Orthogonal Vector-valued Multivariate Wavelet Packets

In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.

Matrix Expression of the Orthogonal Wavelet (Packets) Transform

Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provided yet. In this paper, the formulation to generate the re-lated matrix is put forward and the theorem on the orthogonality of this matrix proved. This effort deploys a basis for more deeper and wider applications in chemical processes. *

Infrared Image Small Target Detection Based on Bi-orthogonal Wavelet and Morphology

An image multi-scale edge detection method based on anti-symmetrical bi-orthogonal wavelet is given in theory. Convolution operation property and function as a differential operator are analyzed,which anti-symmetrical bi-orthogonal wavelet transform have. An algorithm for wavelet reconstruction in which multi-scale edge can be detected is put forward. Based on it, a detection method for small target in infrared image with sea or sky background based on the anti-symmetrical bi-orthogonal wavelet and morphology is proposed. The small target detection is considered as a process in which structural background is removed, correlative background is suppressed, and noise is restrained. In this approach, the multi-scale edge is extracted by means of the anti-symmetrical bi-orthogonal wavelet decomposition. Then, module maximum chains formed by complicated background of clouds, sea wave and sea-sky-line are removed, and the image background becomes smoother. Finally, the morphology based edge detection method is used to get small target and restrain undulate background and noise. Experiment results show that the approach can suppress clutter background and detect the small target effectively.

Fault Diagnosis Model Based on Feature Compression with Orthogonal Locality Preserving Projection

Based on feature compression with orthogonal locality preserving projection（OLPP）,a novel fault diagnosis model is proposed in this paper to achieve automation and high-precision of fault diagnosis of rotating machinery.With this model,the original vibration signals of training and test samples are first decomposed through the empirical mode decomposition（EMD）,and Shannon entropy is constructed to achieve high-dimensional eigenvectors.In order to replace the traditional feature extraction way which does the selection manually,OLPP is introduced to automatically compress the high-dimensional eigenvectors of training and test samples into the low-dimensional eigenvectors which have better discrimination.After that,the low-dimensional eigenvectors of training samples are input into Morlet wavelet support vector machine（MWSVM） and a trained MWSVM is obtained.Finally,the low-dimensional eigenvectors of test samples are input into the trained MWSVM to carry out fault diagnosis.To evaluate our proposed model,the experiment of fault diagnosis of deep groove ball bearings is made,and the experiment results indicate that the recognition accuracy rate of the proposed diagnosis model for outer race crack、inner race crack and ball crack is more than 90%.Compared to the existing approaches,the proposed diagnosis model combines the strengths of EMD in fault feature extraction,OLPP in feature compression and MWSVM in pattern recognition,and realizes the automation and high-precision of fault diagnosis.

A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.

ADMISSIBLE WAVELETS ON THE PRODUCT HEISENBERG GROUP H_n

Let H. be the n-direct proded of Heisenbery group H, P the affine group of Hn. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspaces under unitary representation U for L2(Hn) is given. The restrictins of U on these subspaces are square-integrable. The charactedsation of admissible condition is obtained in ierms of the Fourier transform. By seleting appropriately an orthogonal wavelet basis and the wavelet transform,the authors obtain the orthogonal direct chin decomposinon of function space L2(P,dμl).

Optimal Interpolatory Wavelets Transform for Multiresolution Triangular Meshes

In recent years, several matrix-valued subdivisions have been proposed for triangular meshes. The ma-trix-valued subdivisions can simulate and extend the traditional scalar-valued subdivision, such as loop and subdivision. In this paper, we study how to construct the matrix-valued subdivision wavelets, and propose the novel biorthogonal wavelet based on matrix-valued subdivisions on multiresolution triangular meshes. The new wavelets transform not only inherits the advantages of subdivision, but also offers more resolutions of complex models. Based on the matrix-valued wavelets proposed, we further optimize the wavelets transform for interactive modeling and visualization applications, and develop the efficient interpolatory loop subdivision wavelets transform. The transform simplifies the computation, and reduces the memory usage of matrix-valued wavelets transform. Our experiments showed that the novel wavelets transform is sufficiently stable, and performs well for noise reduction and fitting quality especially for multiresolution semi-regular triangular meshes.

不同容量下并网模式交流微电网短路故障早期检测与区域定位

随着分布式电源(distributed generation,DG)的容量变化,微电网原有的供电结构发生改变,使得潮流大小、方向和功率结构发生变化,对快速检测和定位微电网中的短路故障区域提出了挑战。在MATLAB/Simulink中搭建低压交流微电网模型;通过高尺度小波能量谱算法对微电网与大电网公共连接点(point of common coupling,PCC)处检测到的电流进行分解,提取适应不同容量情况的短路故障特征值,实现了不同容量下微电网短路故障的早期检测;利用小波能量谱特征结合基于正交最小二乘法(orthogonal least square,OLS)的径向基函数(radial basis function,RBF)神经网络算法提出一种适用于不同容量微电网的短路故障区域定位方法,并进行仿真验证;在此基础上设计并网模式微电网短路故障保护硬件系统,并进行实验验证。结果表明,所设计的保护系统能够快速、准确地同时实现并网模式下交流微电网短路故障的早期检测与区域定位。

基于LWT的可见光OFDM-IM系统研究

针对索引调制正交频分复用(OFDM-IM)技术峰均比过高,对相位噪声和载波频偏敏感,系统复杂度高等问题,提出基于小波提升变换(LWT)的可见光OFDM-IM系统。首先选择正交小波基作为子载波,通过对信号的分裂、预测和更新,将信号分为高频信号和低频信号,再结合可见光信道构成LWT-OFDM-IM系统,最后通过理论分析和蒙特卡罗方法对系统的可靠性、峰均比特性和最佳小波分解层数进行了仿真验证,结果表明:当子载波N=256,子块中子载波数量L=4,激活子载波数量k=2,系统误码率为10~(-4)时,LWT-OFDM-IM比FFT-OFDM-IM改善约8 dB,相较于DWT-OFDM-IM提高约4 dB。当系统互补累计分布函数(CCDF)为10^(-1)数量级时,LWT-OFDM-IM的峰均比较FFT-OFDM-IM改善约2.3 dB。随着小波层数的递增,系统的误码性能越好,当小波层数为3层时,大约在10 dB附近,误码率可到10^(-5)量级。

斯里兰卡极端降水时空演变特征及趋势预测

斯里兰卡是中国“一带一路”倡议的重要节点国家,极端降水对当地社会经济威胁较大,极易引发灾害。选取当地10个气象站2008—2020年的逐日降水资料,基于RClimDex模型计算斯里兰卡6个极端降水指标,利用经验正交函数分析、Morlet小波分析和重标极差法(R/S分析)等,分析极端降水事件的时空演变特征。结果表明:极端降水指数在时间分布上,除持续干旱指数(CDD)呈减少趋势外,其他各指数均为上升趋势;极端降水指数空间差异表现为北部沿海平原地带的极端降水强度高于南部沿海平原,拉特纳普勒市以西地区为斯里兰卡降水事件的多发区;极端降水指数周期性明显,绝大多数极端降水指数以6~7 a为第一主周期。R/S分析表明当地极端降水事件未来持续可能性较大。研究成果可为斯里兰卡极端气候预测、生态环境保护、防灾减灾工作等提供决策支持。

青海省多年地表感热通量的时空变化特征

选取青海省35个气象站观测数据,基于CHEN-WENG感热系数方案,计算了1980—2017年青海省地表感热通量。利用小波分析、Mann-Kendall突变检验和经验正交函数法(Empirical Orthogonal Function,EOF),对感热通量的时空变化特征及其影响因子进行分析。结果表明:(1)1980年以来,青海省全年和各季节感热通量总体上均呈上升趋势,并具有28 a的主周期和约18 a的副周期,冬季的周期变化较为复杂;(2)全年和各季节感热通量与地气温差存在显著相关性,2004—2017年受地气温差增大的影响上升;(3)全年、春季和秋季感热通量与风速存在显著相关性,1980—2004年受风速减小的影响感热通量下降;(4)夏季降水与感热通量呈显著负相关;(5)从空间上看,全年以及春季感热通量呈现出显著的东西分异,秋、冬季表现出一定程度的南北分异。

基于相对湿润指数的浙江省茶叶气象干旱特征分析

【目的】研究浙江省茶叶气象干旱的演变规律,为茶叶安全生产优化布局提供科学依据。【方法】利用浙江省68个地面气象观测站50 a(1971—2020年)的逐日气温、降水量、日照时数等数据,基于相对湿润指数、正交经验函数和小波分析法等分析浙江省茶叶气象干旱的时空分布规律。【结果】浙江省茶叶生产夏季干旱的强度和发生频率高于秋季,且均呈现西高东低的分布,中西部尤其金衢盆地的干旱强度和频率为全省最强,浙北地区次之,沿海地区最小。茶叶夏季干旱站次比呈逐年下降的趋势,秋季则呈现先升后降的趋势,2000年以后夏秋两季出现极端大范围茶叶气象干旱的年份增多。茶叶夏季和秋季干旱强度的正交经验函数第一模态表现为全省变化一致性,第二模态中沿海局部地区和内陆呈反相位变化,夏秋两季干旱强度的主模态时间序列分别存在2-6、2-4、6-10 a的振荡周期。【结论】浙江省在夏季和秋季出现茶叶气象干旱的频率在下降,但出现极端干旱的概率在增加,应重点加强茶叶主产区干旱监测预警能力建设,提升防旱抗旱能力。