Wavelet transforms: Application to data analysis - I

In this article, we elaborate upon the key ideas underlying the construction of various wavelet basis sets. The roles of translation and scaling, which enable the wavelets to localize variations at desired levels of resolution, are clearly brought out. After explaining the implementation of one dimensional wavelet transform, we illustrate their usefulness through the analysis of a data set.     

小波分析和小波包在图像压缩中的应用

小波和小波包对图像压缩都是十分有用的工具,小波包理论是在小波基础上发展起来的时频分析理论,在图像压缩中取得了较好的应用。文中介绍了小波分析和小波包的基本理论,分析了基于小波和小波包进行图像压缩的方法,利用MATLAB 7对相同图像进行了计算机仿真,并对仿真结果进行了分析。实验表明,小波包压缩后的效果比小波更好。     

基于小波分析的GPS动态监测数据变形特征分析方法

主要对小波分析的一些基本数学理论进行了详细的介绍,并对小波变换以及多分辨率分析进行了重点且深入的分析。在此基础上,通过实际数据试验研究了小波基函数的选取,以及软、硬阈值处理方式对GPS变形数据序列去噪效果的影响,得到一些有益的结论。还对小波分解的噪声特性进行了详细分析,在此基础上通过实例验证了基于小波分析方法对GPS动态监测数据进行变形特征特征提取的可行性和可靠性,得出了其提取结果要优于中值滤波方法进行提取的结论。     

小波阈值方法在Laplace方程中的应用

把Laplace方程的柯西问题化为算子方程来考虑,右端项是非精确数据。运用小波对偶最小二乘法,得到了阶最佳的收敛性稳定性分析和非线性自适应。     

小波分析在矩量法中的应用

将小波分析同矩量法相结合,首先,讨论了周期小波在电磁散射问题中的应用,并指出随着目标电尺寸的增大,该方法产生一个庞大而病态的阻抗矩阵,结果大量的计算机资源因此而耗费。其次,提出周期小波的两种改进算法,其中物理光学预处理算法改善了阻抗矩阵的病态性,降低了矩阵维数,提高了计算速度。     

基于小波多分辨分析图像水印技术的一种算法

本文提出一种基于DWT域的图像水印算法。该算法利用内嵌零树小波图像压缩算法,将二进制水印内嵌到按零树小波系数排序的最重要系数中。文末对该算法进行了仿真验证、峰值信噪比(PSNR)和归一化相关系数(NC)说明。该算法可以在保持图像质量的同时获得较大的鲁棒性。     

复数小波变换在图像匹配中的应用

本语言介绍了一种新的基于多分辩率的层次分配方法,即利用复数小波变换作为分层的手段。小波变换的聚焦作用,可以分析到图像的任何细节,而复数小波变换所具有Gabor变换的特征,可以考察经分层后的信号的各个方向的细节。     

Secondary analysis of large-scale assessment data: an alternative to variable-centred analysis

International large-scale assessments are now part of the educational landscape in many countries and often feed into major policy decisions. Yet, such assessments also provide data sets for secondary analysis that can address key issues of concern to educators and policymakers alike. Traditionally, such secondary analyses have been based on a variable-centred approach that gives rise to league tables. In the study reported here, a person-centred analysis is used as an alternative to the traditional approach. Data from the International Civic and Citizenship Education Study (ICCS) were analysed to investigate Asian students' attitudes to their future civic participation. Cluster analysis with validity measures showed that 4 distinct groups of students were identified within the societies studied thus highlighting the diversity within the samples. These results cannot be achieved with a conventional variable approach to analysis, and they suggest the usefulness of exploring alternative approaches to secondary data analysis.     

小波包在旋转机械故障诊断中的应用

根据旋转机械故障振动信号的特点，提出了应用小波包分解、重构技术进行消噪处理及频带能量故障特征提取的方法，实验分析结果表明该方法可以有效地提高故障诊断的抗干扰能力和故障诊断的准确性。     

浅谈Excel趋势线在生物学实验数据分析中的应用

趋势线是Excel提供的数据分析工具,利用趋势线拟合,构建数学模型,进行生物学实验数据分析,具有方便快捷的优点。本文就生物学实验常见数据拟合方式如线性拟合、指数拟合等展开讨论。     

Application of data envelopment analysis on the indicators contributing to learning and teaching performance

This paper applies data envelopment analysis (DEA) to explore the quantitative relative efficiency of 18 classes of freshmen students studying a course of English conversation in a university of Taiwan from the academic year 2004-2006. A diagram of teaching performance improvement mechanism is designed to identify key performance indicators for evaluation in order to help teachers concentrate their efforts on the formulated teaching suggestions. The sensitivity study highlights the priority of the richness of course contents over the other evaluated indicators. The performance improvement mechanism can help decision-makers to design educational policies.     

小波分析及其在电力系统暂态分析中的应用

小波分析为电力系统故障分析提供了强有力的数学工具,本文对小波变换在电力系统故障分析中的应用进行了综述,展示了一些新思路,也提出一些需要进一步完善的思路。     

统计分析中对应分析方法应用

通过数学方法的描述和统计软件SPSS对实例的分析,阐明了在统计分析中运用对应分析方法,可以得出正确的探索性统计分析结果,直观地揭示统计数据间的内在联系。     

Excel在物理实验数据处理中的应用研究

以霍尔器件测量磁感应强度实验为例,介绍Excel分析处理物理实验数据的方法。利用Excel处理物理实验数据不仅快捷准确,免除了大量繁杂的运算工作,而且方法简便,结果可视,且可随着输入数据即时更新。经过几年来在物理实验教学当中的应用,表明该方法在实现学生实验数据的管理和分析处理方面非常有效。     

小波变换技术在音频压缩中的应用

小波(W avelet)变换是当前信息处理领域中发展非常迅速的新技术,它同时具有理论深刻和应用广泛的双重意义。由于小波变换具有传统的DCT正交变换的能量紧致性,同时还具有与人类视听觉系统很相似的特性,因此在音视频压缩领域受到广泛关注。Haar小波是小波函数簇中的一个基本函数,应用于音频信息压缩,不仅可以获得较高的压缩比,而且压缩后又能有效保留原始音频信息的状态特征参数,因此为进一步高效处理音频信息提供了一种可行的方案。     

PSD在超精密加工实验数据分析的应用

功率谱密度(power spectral density,PSD)用于描述随机过程的功率随频率的分布。在超精密加工实验中,功率谱方法不仅仅用于切削力信号分析,还可以用于超精密加工表面微观形貌分析;既可以反映出不同频率在表面形貌中所占的比重,还可揭示切削参数、工件材料性能等对超精密加工表面生成的影响程度。该文使用PSD方法对超精密飞刀铣削在不同进给速度下加工不同工件材料的实验结果进行分析,结果表明,相比于表面粗糙度参数来说,PSD方法更有利于表现出工件材料对超精密加工表面的影响。     

小波变换及相关系数在超声脉冲回波消噪中的应用

小波分析在超声信号处理上已得到广泛的应用．基于消失矩及分解尺度对重构信号恢复程度的影响,把相关系数作为判断脉冲回波信号处理好坏的依据,用数学软件Matlab7．0编程,经小波变换和Fourier变换处理后的重构信号与原始信号比较可以得出,对信噪比较小的非平稳信号用小波分析处理效果较好,且参数不同信号的恢复效果不同．     

The RC circuit: An approach with Fourier transforms

In this article we shall mathematically analyse the Resistor-Capacitor (RC) circuit with the help of Fourier transforms (FT). This very general technique gives us a lot of insight into solving first order differential equations with source terms depending on time. In itself, the RC circuit is by far the most commonplace entity in modern electronics. But the method of FT is not the accepted custom for an electronic engineer, who is probably more comfortable working with complex impedances and phasors while solving problems in network analysis. In fact, what is used much more extensively is the Laplace transform. But a lot of things, (including the complex impedance itself, and some insight into complex analysis) can be understood better if we use the FT approach to solve the differential equations that come up in network analysis. The use of FT comes smoothly from first principles — precisely what we set out to demonstrate here.