α尺度多重双正交小波包的L2(R)分解

小波包的方法能对高频信号进行小波分解,给出了频域带更精细的划分。本文研究α尺度多重双正交小波包的性质,讨论α尺度多重双正交小波包的分解,给出L^2(R)的双正交基。     

正整数伸缩的双正交双向小波包

本文引入了尺度为α的双正交双向小波包的概念,运用矩阵理论和算子理论研究了双正交双向小波包的性质。得到构造双正交双向小波包的一种新方法。建立了进行迭代与分解的公式。利用双正交双向小波包,得到空间L~2(R)新的Riesz基。最后,给出构造双正交双向小波包的例子。     

双正交小波矩阵

本文引进了双正交（半正交）小波矩阵及对偶的概念。讨论了这些矩阵的一些性质，尤其是给出了利用小波矩阵的元素将离散函数展开为级数形式的结果，进而建立了半正交小波矩阵与［８］中正交小波矩阵，双正交小波矩阵与对偶双正交小波矩阵的关系。最后举例说明了本文引进双正交（半正交）小波矩阵及对偶概念和方法的合理性。     

a尺度正交的多尺度函数的构造

给出α尺度正交多尺度函数一种新的构造方法。α尺度正交的多尺度函数可由任意α尺度正交的单尺度函数及滤波器组构造出来的。由于α尺度单正交尺度函数选取的任意性和用于构造的滤波器组具有相当大的自由度,从而使得有可能构造出大量的具有很好性质的α尺度的多尺度函数,进而得到良好性质的多小波。     

半正交小波包

给出紧支撑多元半正交小波包的构造算法。该小波包的特点是：分解系数的选取具有多样性,并且该小波包是基本小波包推广的广义小波包。利用该小波包可使L^2(R^s)中小波基的选择更灵活。     

2重正交多尺度函数和多小波的构造

基于正交单尺度函数,给出一种构造2重正交多尺度函数的方法。也给出对应正交多小波的显式构造公式。由于构造的2重正交多尺度函数中的个是所给的正交单尺度函数,另一个是新构造出的函数,因此这种多小波比相关的单小波具有更好的频率局部性。     

混合正交小波包

给出了尺度因子a=4时混合正交小波包的构造,传统的小波包可以细化频谱窗口以解决正交小波基在高尖区频谱局部性差的缺点,在混合正交小波基的基础上构造出的混合正交小波包不仪具有传统小波包的特点,而且在不失正交性的条件下,改变了小波包函数的形状,从而获得更好的细节匹配。     

紧支撑二元正交小波

高维小波是处理多维信号的有力工具,张量积小波有其自身的缺点.本文给出构造矩阵伸缩为2I的紧支撑二元正交尺度函数的一种算法,得到相应的小波函数.当参数l1,l2不全为零时,构造出的小波函数为不可分的,最后给出算例.     

一类紧支撑对称双正交小波

摘要:研究伸缩因子为3紧支撑对称双正交小波的构造问题.任给一个插值对称的加细函数,本文提供 一个构造其对偶尺度函数的迭代算法,其对偶尺度函数的正则性可以达到任意水平,讨论了它的一些性 质,如对称性和衰减性.最后,给出构造算例.     

设计地震波的小波包多尺度调整

提出了一种基于小波包对地震动在不同尺度上进行调整的方法。和传统的小波分析相比，该方法不仅对地震波低频分量进行精确调整，还可对其高频成分实现类似的调整。本文提出的方法可方便地应用于时频联合分析和结构抗震设计中。     

Toward a liquid-state theory with accurate critical-region behavior

A scaling-theory approach that yields the scaled thermodynamics in the critical region as the solution of an ordinary differential equation is given, along with a power-series isocline representation of the solution yielding a polynomial fit of a high accuracy. A means of extending the approach to the whole liquid-state region through a self-consistent integral equation for the radial distribution function is discussed. An alternative integral-equation approach and a simple application of scaling-theory results that has already been found to be globally useful are also noted.Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

A Nontrivial Solution to a Stochastic Matrix Equation

If A is a nonsingular matrix such that its inverse is a stochastic matrix, the classic Brouwer fixed point theorem implies that the matrix equation AXA = XAX has a nontrivial solution. An explicit expression of this nontrivial solution is found via the mean ergodic theorem, and fixed point iteration is considered to find a nontrivial solution.     

Further Solutions of a Yang-Baxter-Like Matrix Equation

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, and an infinite number of solutions that commute with any given complex square matrix A are found. Our results here are based on the fact that the matrix A can be replaced with its Jordan canonical form. We also discuss the explicit structure of the solutions obtained.     

Realization of Radiance Temperature Scale from 500K to 1,250K by a Radiation Thermometer with a Thermal Detector

The radiance temperature scale from 500K to 1,250K was realized by using a thermal detector transfer reference thermometer (TRT) with its spectral response centered at 3.9μm. The TRT is calibrated at the four fixed points of tin, zinc, aluminum, and silver, and the scale is obtained by interpolation with Wien’s equation, Planck’s equation, the Sakuma–Hattori (SH) formula, and a Planckian SH (PSH) formula. The interpolation uncertainty dramatically decreases as the physical model for the interpolation equations becomes more realistic. The uncertainty of the scale is evaluated, including the repeatability of the calibration and the long-term stability of the TRT over a period of more than 20 months. The realized scale over part of the interpolation region was validated by comparing it with the ITS-90, resulting in excellent agreement within 0.09 K. The resulting uncertainty of the realized scale varies from 0.06K to 0.38K (k = 1), depending on the temperature.     

瑞利衰落信道下差分跳频通信系统抗部分频带噪声干扰的性能分析

在瑞利衰落信道和部分频带噪声干扰共存的环境下,针对逐符号检测和按序列检测两种信号检测方法,分别就差分跳频通信系统的误符号性能进行了理论分析,同时做出相应的计算机仿真.结果证实,差分跳频通信技术和按序列检测方法的结合,使通信系统的抗部分频带噪声干扰的性能得到了比较显著的提升.     

紧支对称准正交小波的正则性

介绍了准正交滤波器及其小波,以及正则性的3个命题。运用尺度函数正则性命题分析了长度为2N的准正交小波的正则性,得到正则指标值.对于N=3,4,5,正则指标分别是α3=1.546 4,α4=1.446 4和α5=1.571 0.     

有限区域上的二维多小波基

加细方程在小波的构造中起着非常重要的作用。本文基于定义在二维平面上的矩阵加细方程及二维伸缩与平移算子理论构造出有限区域上的多分辨分析及二维多小波基。最后给出构造算例。