Least square method based on Haar wavelet to solve multi-dimensional stochastic Ito-Volterra integral equations

This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Ito-Volterra integral equation.This approach is to transform stochastic integral equations into a system of algebraic equations.Meanwhile,the error analysis is proven.Finally,the effectiveness of the approach is verified by two numerical examples.

BLIND SYMBOL RATE ESTIMATION OF SATELLITE COMMUNICATION SIGNAL BY HAAR WAVELET TRANSFORM

As the raised cosine shaping filter is often employed in practical satellite communication system,the envelope fluctuation at the symbol transition point is decreased which leads to the failure of the common wavelet algorithm under low SNR.Accordingly,a method of blind symbol rate estimation using signal preprocessing and Haar wavelet is proposed in this paper.Firstly,the effect of filter shaping can be reduced by the signal preprocessing.Then,the optimal scale factor is searched and the signal is processed and analyzed by the Haar wavelet transform.Finally,the symbol rate line is extracted and a nonlinear filter method is inducted for improving the estimation performance.Theoretical analysis and computer simulation show the efficiency of the proposed algorithm under low SNR and small roll-off factor.

Wireless Transmission Based Image Quality Analysis Using Uni-Level Haar Wavelet Transform

This article deals with picture excellence examination by different parameters utilizing uni-level Haar wavelet transmission in excess of remote channel. The quality is analyzed based on power. The goal is towards reducing absolute power assigned in favour of picture compression and communication, while power in favour of every bit is reserved at prearranged value. Two Power Algorithms were presented. The greatest iterative power control calculation and Minimum Power Adaptation Algorithm (MPAA) are proposed. Those algorithms methodology was utilized for improving the aggregate power dispensed for multimedia such as picture because of input compression and transmission focus towards a settled bit source mutilation. Simulations were performed utilizing Haar wavelet than Additive White Gaussian Ration (AWGN) channel. Different picture excellence parameters, for example, Peak Signal to Noise Ratio (PSNR), M-Normalized Cross-Correla- tion, Average Difference;Structural Content parameters, for example, Maximum Difference, Normalized Absolute Error, Elapsed Time, CPU time, demonstrate a improved presentation with MPAA, Maximum Power Adaptation Algorithms (MAPAA) instead of Conventional Power Adaptation Algorithm (CPAA).

Efficient Numerical Scheme for the Solution of HIV Infection CD4^(+)T-Cells Using Haar Wavelet Technique

In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells model.In this technique,the derivative in the nonlinear model is approximated by utilizing Haar functions.The value of the unknown function is obtained by the process of integration.Error estimation is also discussed,which aims to reduce the error of numerical solutions.The numerical results show that the method is simply applicable.The results are compared with Runge-Kutta technique,Bessel collocation technique,LADM-Pade and Galerkin technique available in the literature.The results show that the Haar technique is easy,precise and effective.

THREE-DIMENSIONAL ANALYSIS OF FUNCTIONALLY GRADED PLATE BASED ON THE HAAR WAVELET METHOD

有材料性质的任意的分布的一个简单地支持的机能上地分级的矩形的盘子的三维的分析基于 Haar 小浪用一个简单、有效的方法被做。与在对待奇特的好特征， Haar 系列答案为任意的分布很快收敛，特别为材料性质在一些区域很快变化的盒子。通过数字例子，到机械刺激的板的结构的反应上的顶和底部表面和不同材料坡度分布上的材料常数的比率的影响被学习。

An Implementation of Haar Wavelet Based Method for Numerical Treatment of Time-fractional Schrdinger and Coupled Schrdinger Systems

The objective of this paper is to solve the timefractional Schr¨odinger and coupled Schr¨odinger differential equations(TFSE) with appropriate initial conditions by using the Haar wavelet approximation. For the most part, this endeavor is made to enlarge the pertinence of the Haar wavelet method to solve a coupled system of time-fractional partial differential equations. As a general rule, piecewise constant approximation of a function at different resolutions is presentational characteristic of Haar wavelet method through which it converts the differential equation into the Sylvester equation that can be further simplified easily. Study of the TFSE is theoretical and experimental research and it also helps in the development of automation science,physics, and engineering as well. Illustratively, several test problems are discussed to draw an effective conclusion, supported by the graphical and tabulated results of included examples, to reveal the proficiency and adaptability of the method.

Phase-domain blind estimation of symbol duration based on Haar wavelet transform

A phase-domain blind estimator of symbol duration based on Haar wavelet transform(HWT) is proposed.It can estimate the symbol duration of phase modulated signals,such as M-ary phase-shift keying(MPSK) signals and polyphase coded signals.The closed form of the spectrum of HWT is derived.Theoretical analysis shows the frequency of the first spectral peak is equal to the symbol rate,which is the reciprocal of symbol duration.Thus the symbol duration can be extracted from the spectrum.Subsequently,the optimum wavelet scale is determined according to the maximum output signal to noise ratio(OSNR) criterion.MAT-LAB simulations show that this algorithm can blindly estimate the symbol duration without any prior knowledge.This estimator need not estimate the carrier frequency and has the characteristics of low computation complexity and high accuracy.

Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems

Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems. Through this analysis, solutions are found on the coarse grid points and refined towards higher accuracy by increasing the level of the Haar wavelets. A distinctive feature of the proposed method is its simplicity and applicability for a variety of boundary conditions. Numerical tests are performed to check the applicability and efficiency. C++ program is developed to find the wavelet solution.

Haar wavelet discretization method for free vibration study of laminated composite beam under generalized boundary conditions

Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elastic boundary condition(BC)by using Haar wavelet discretization method(HWDM).Timoshenko beam theory is utilized to model the free vibration of LCB.The LCB is first split into several segments,and then the displacement for each segment is obtained from the Haar wavelet series and their integral.Hamilton’s principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB.The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works.Numerical results are shown graphically and demonstrate the validation of our method.

基于Haar小波的双直线电机自适应滑模控制

针对双直线电机伺服系统的同步控制精度易受耦合干扰、负载扰动和模型不确定性等因素影响,提出了一种基于Haar小波逼近的自适应滑模同步控制方法。采用滑模位置控制器克服扰动对伺服系统的影响,提高抗干扰性能;为削弱滑模控制引起的系统抖振,采用Haar小波基函数逼近系统动态模型中的时变非线性函数,进一步提高系统鲁棒性;同时采用自适应算法在线整定逼近函数的权值,并基于Lyapunov稳定理论证明了控制系统的渐进收敛性。实验结果表明,基于Haar小波的自适应滑模控制与滑模控制相比,不仅提高了系统的跟踪精度和同步精度,还增强了系统的鲁棒性。

Complete quantum circuit of Haar wavelet based MRA

Wavelet analysis has applications in many ar- eas, such as signal analysis and image processing. We pro- pose a method for generating the complete circuit of Haar wavelet based MRA by factoring butterfly matrices and con- ditional perfect shuffle permutation matrices. The factoriza- tion of butterfly matrices is the essential part of the design. As a result, it is the key point to obtain the circuits of I 2t ⊕ W ⊕ I 2n ? 2t ?2. In this paper, we use a simple means to de- velop quantum circuits for this kind of matrices. Similarly, the conditional permutation matrix is implemented entirely, combined with the scheme of Fijany and Williams. The cir- cuits and the ideas adopted in the design are simple and in- telligible.

基于Butterworth滤波和Haar小波变换的干涉图像齿面域分割

干涉图像中反映齿面形貌信息的齿面域被背景噪声包围,其分割精度对相位解包裹、图像配准等后续的处理步骤存在较大的影响,直接关系到最终测量结果的精度。针对齿面干涉图像边界存在杂散条纹的现象,通过分析齿面干涉条纹的分布规律,提出了一种结合Butterworth滤波和Haar小波的齿面域分割方法。最后,在本文实验条件下,通过与时域分割方法进行对比,该方法可以将齿面干涉图像的边界杂散条纹区域内解包裹相位值有错误的地方排除在有效测量区域外并且能够对其进行有效校正,证明了基于频域信息的分割方法能够有效地提高干涉图像齿面域分割的精度。

An Improved r-Adaptive Galerkin Boundary Element Method Based on Unbalanced Haar Wavelets

An r-adaptive boundary element method(BEM) based on unbalanced Haar wavelets(UBHWs) is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To accelerate the convergence of the adaptive process,the grading function and optimization iteration methods are successively employed.Numerical results of two representative examples clearly show that,first,the combined iteration method can accelerate the convergence;moreover,by using UBHWs,the memory usage for storing the system matrix of the r-adaptive BEM can be reduced by a factor of about 100 for problems with more than 15 thousand unknowns,while the error and convergence property of the original BEM can be retained.

应用小波通道注意力网络的地震数据重建方法

重建缺失的地震道是地震数据处理的关键环节之一。近年来提出了多种基于深度学习理论的地震数据重建方法。然而,这些方法中常用的卷积运算只能捕捉到地震数据的局部特征,没有充分利用全局信息。另外,池化操作也会造成特征图信息的丢失,从而破坏地震反射的细节特征。为此,提出了基于小波通道注意力网络的地震数据重建方法。哈尔(Haar)小波变换能够有效提取信号的多尺度特征,并在上采样过程中避免信息的丢失;高效通道注意力模块通过对不同通道特征图之间的相关性进行建模,能实现全局信息的充分利用。合成和实际地震数据的实验结果表明,与具有代表性的深度学习方法相比,文中所提出的网络模型可以产生更准确的重建结果。

基于信息熵和Haar小波变换的开关电流电路故障诊断新方法

针对开关电流(SI)电路的故障诊断和定位问题,为进一步提高故障准确率,提出了基于信息熵和Haar小波变换的开关电流电路故障诊断新方法。该方法采用伪随机信号激励经蒙特卡罗分析、Haar小波正交滤波器分解和信息熵及模糊集的计算来实现故障特征的提取,以减少信号的冗余。最后构建故障字典,完成各故障模式的故障分类。对六阶切比雪夫低通滤波器进行了仿真实验验证,获得了100%的故障诊断准确率,与其它方法进行比较,实验结果显示了本文方法的优越性。

基于Haar小波变换的信号到达时间估计

研究了在信号频率、初相、幅度未知条件下,矩形包络复正弦信号的到达时间估计算法。先利用相关检测算法,对信号的起止时间进行粗估计。在检测到信号的条件下,估计出信号频率并将其变换至基带,在一定尺度下对基带信号作Haar小波变换,检测出小波变换模值的峰点位置作为到达时间精估计。给出了小波尺度选取的原则,并推导了到达时间估计的克拉美罗限(CRLB)。计算机仿真表明,信噪比达6 dB时,到达时间估计的均方根误差小于0.8倍的采样间隔,实现了对信号到达时间的精估计。

基于Haar小波变换和分块DCT的人耳识别

提出一种新的对人耳图像进行降维的方法。先对人耳图像进行二维的离散小波分解,然后再对小波分解后得到的低频信息施行分块离散余弦变换,进而获得图像的特征向量。实验证明,该方法与模式识别领域中广泛应用的PCA-LDA方法相比,在识别率大体相当的前提下,具有计算量小、降维速度快的优点,是对人耳图像进行特征提取的一种有效的手段。

基于多尺度Haar小波变换的MPSK信号码速率盲估计

研究了相位编码信号的码速率估计,提出基于Haar小波变换的多尺度MPSK信号码速率盲估计方法。首先对接收信号作FFT得到信号频谱,对频谱进行平滑之后估计其中心频率,接着由估计出的频率构造相关接收机;然后估计信号的3dB带宽,由估计的带宽作为参考选取三个小波尺度,利用Haar小波的边缘检测特性对相关接收机的输出进行多尺度码元相位跳变点检测,多尺度检测的结果进行叠加;最后对叠加的结果作DFT估计频率得到MPSK信号的码速率估计。仿真表明,高于信噪比门限时本算法可以对码速率进行有效估计。

Haar小波运算矩阵与性质在分布参数系统控制中的应用

在小波理论的基础上,给出了Haar小波基所对应的乘积运算矩阵fm×m、元素乘积矩阵Hm×m、乘积积分运算矩阵W、微分运算矩阵D等,并给出了Haar小波逼近运算性质。将这些矩阵及其性质应用到分布参数系统控制问题的求解过程中,取得了较好的效果。