波函数

Then the relationship between the wavelet shrinkage and diffusion equation is studied. A t last stationary wavelet transform has been used to derive an affine invariant function.

同时从小波阈值函数与散度函数的关系入手进行研究，说明了小波分析与偏微分方程之间的联系。

The Absolute Wavelet Affine Invariant Function is constructed based on WAIF,and is used as the eigenvector of the object to be recognized,and is combined with Convex Hull for object recognition.

基于小波仿射不变函数构造了绝对小波仿射不变函数，作为待识别目标的特征向量，与凸壳相结合进行目标识别。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

along with the development of digital technology,digital filters are widely used in many fields,this paper introduces how to design a iir digital notch filters in matlab environment.the design of digital notch filters can be achieved through three steps:firstly,the design of analog lowpass filter; secondly,it is analog lowpass to analog band stop filter conversion;at last,using the bilinear transformation make the analog notch filters change into digital notch filters.the paper also introduces how to design the transfer function of the digital notch filters using all the zeros and farthest points at the same time,it also introduces the program of the digital notch filters under butterworth analog lowpass prototype.

摘 要：随着数字技术的发展，数字滤波器在许多领域得到广泛的应用。研究一种在matlab语言环境下设计iir数字陷波滤波器的方法，在数字陷波滤波器设计过程中，先进行模拟低通滤波器的设计，然后进行模拟低通/模拟带阻滤波器转换，最后采用双线性变化法将模拟陷波滤波器转化成数字陷波滤波器。提出一种用所有零点和极点来表达数字陷波器传递函数的方法，同时给出以巴特沃斯模拟低通为原型设计数字陷波滤波器的程序。关键词：无限冲激响应；巴特沃斯滤波器；数字陷波滤波器；matlab；双线性变换

When seismic wavelet is in non-minimum phase , we can make it have smaller phase by doing exponential weighting . As for nonwhite noise problem of reflection coefficient , we may employ logarithmic power spectrum to estimate the autocorrelation function of seismic wavelet , then obtain seismic wavelet and deconvolution opera .

当地震子波为非最小相位时，可利用指数加权方法使之小相位化；对于反射系数非白噪声问题，本文提出利用对数功率谱来估算地震子波的自相关函数进而求取地震子波以及反褶积算子的方法；对于理想的期望子波，本文采用"宽带雷克子波"作为期望输出子波。

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction.

本文围绕地球重力场的球面小波展开及其应用进行研究，在积分逼近与径向基函数概念的基础上引入了球面小波，利用球面小波对重力场展开进行了重新表示，在此基础上进行了球面小波正则化、卫星重力多尺度逼近、航空重力数据向下延拓、重力场球面小波逼近的最小范数性质、两类边值问题的球面小波实用解、球面选择多尺度去噪方法等方面的研究。

By using the least square method and the weighted functionmethod of nonparametric estimation together, this paper defines the wavelet estimators of β and g.

本文采用了半参数估计常用的办法之一——最小二乘法结合非参数权函数估计法定义了参数分量和非参数分量的估计，这里的权函数不是通常所采用的核权函数或近邻权函数，而是由小波方法所得到的权函数，我们称它为小波权函数。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesn't calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesnt calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

Based on orthogonal function unfolding theory, the transverse fields can be represented as a superposition of waveguide modes. And according to coupled-wave theory, the time-dependent multi-mode coupling-wave equations (or the generalized telegrapher's equations) and the coupling coefficients among the different modes were deduced. The generalized telegrapher's equations are a set of coupled one-dimensional partial differential equations for the amplitudes of the modes.

应用正交函数的展开理论，将变截面波导中的电磁场表示为横电波和横磁波本征模式的级数；然后根据耦合波理论，推导了考虑波导金属壁有限电导率的变截面波导时域多模耦合波方程组及各模式间耦合系数的表达式。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。