双线性

A design method of switched-currentladder filters using the bilinear transformation is proposed.

开关电流梯形滤波器的双线性变换设计孟相如，邱关源（西安交通大学电气系，西安710049）本文提出了一种用双线性变换进行开关电流梯形滤波器设计的方法。

We proposed the simplest structure of 2-D bilinear transformation digital circuit, we proposed four approaches of the realizations:(1) Realization of 2-D discrete domain difference equations;(2) 2-D FFT realization;(3) Digital hardware implementation;(4) by 2-D recursive digital structure to realize them.

在第七章，我们则重点研究了二维数字滤波器的实现问题。我们对第六章提出的2-D双线性变换电路又作了进一步的简化，获得了一种最简结构的二维双线性变换数字电路，该电路仅有二个延时器和一个乘法器。在第七章里，我们提出了二维跳耦型数字滤波器的四种实现方法：(1)二维时域差分方程实现；(2)二维FFT实现；(3)数字硬件实现，(4)用2-D递归数字结构实现。

Abstraction :This paper analyzes the principle of Butterworth digital filter,discuss bilinear transformation method of filter design;record a piece of voice by Microsoft voice recorders, carry on its a time-domain analysis, spectral analysis;then design a specified Butterworth band-stop filter based on the theory of bilinear transform,analyze the filter by the tool named Fvtool;and filter the voice signal acquired by voice recorder.finally compare its characteristics of frequency domain and time domain,study the applications of Butterworth filter in digital signal processing ,in particular in signal denoising.

本文分析了巴特沃思数字滤波器的原理，探讨了双线性变换法设计滤波器的方法；用微软录音机采集一段语音，对其进行了时域分析，频谱分析；然后使用双线性变换法设计了一个的巴特沃思带阻滤波器，并且使用fvtool对设计的滤波器进行分析；然后利用该滤波器对采集的语音信号进行滤波。最后对比滤波前后的语音信号的时域和频域特性，研究了巴特沃思滤波器在信号处理尤其是信号滤波去噪方面的特性和应用。

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

The result shows: the maximum of the exchange bias field moves towardsthe easy axis with increasing the biquadratic coupling field or bilinear coupling field;additionally, the oscillations of the curves for the angular dependence of exchangebias field become weak and gradually resembles the sine function with increasing thebiquadratic coupling field.

结果发现：双线性耦合或双二次耦合的增加都可使交换偏置场的最大值位置向易轴方向靠近，并且双二次耦合的增加使交换偏置场随外磁场的角度变化曲线的振荡也随之减弱，变为类似于正弦函数的图象。

Libermann.The early researcheson this kind of manifolds were closely related to Physics and Mechanics.But since1991,S.Kaneyuki published his result on the algebraic condition for the existence ofinvariant〓structures on a coset space,Lie theory has played the most impor-tant role in the study of this kind of manifolds.In particular,dipolarizations in a Liealgebra are closely related to the homogeneous〓manifolds.Dipolarizationsin semisimple Lie algebras and the homogeneous〓manifolds associated withthese dipolarizations have been studied by S.Kaneyuki,Z.X.Hou and S.Q.Deng.Inthe partⅡ of this thesis we study the dipolarizations in some quadratic Lie algebrasand the homogeneous parakahler manifolds associated with these dipolarizations.

Libermann给出的，早期的有关类流形的研究与物理和力学密切相关，自从1991年金行壮二发表了陪集空间上存在不变仿凯勒结构的代数化结果后，李群及李代数理论在这类流形的研究中起着主要作用，特别地，李代数的双极化与这类流形密切相关，半单李代数的双极化的相关几何，金行壮二，候自新和邓少强等人已作了研究，二次李代数是比半单李代数更广且带有非退化不变双线性型的李代数，本文主要研究了二次代数的双极化及相关几何。

We develop and apply the Hirota bilinear-θfunction method,Jacobi elliptic function expansion method,linear superposition method and F-expansion method respectively to solve many 2+1 dimensional nonlinear wave models including 2+1 dimensional 2DsG equation,the coupled ZK equation,2+1 dimensional KdV equation,2+1 dimensional long wave short wave resonance interaction equation and 2+1 dimensional dispersive long wave equation,abundant Jacobi elliptic function doubly periodic solutions are derived.These solutions show various periodic wave shapes and special periodic characters.

发展和应用Hirota双线性-θ函数方法，雅克比椭圆函数展开法，线性叠加法，F-函数展开法等分别求解2+1维2DsG方程，耦合ZK方程，2+1维KdV方程，2+1维长波短波共振相互作用方程，2+1维色散长波方程，获得丰富的雅克比椭圆函数双周期波解，描述了一些周期波形态及周期特性。

How to easily and reasonably determine the value of principal stress in the direction of plane strain is the key point.

基于弹塑性理论及土的试验规律，在平面应变的简单加载条件下，假定主应力之间的关系为双线性函数，并利用一维固结和破坏时的主应力状态，确定双线性函数的系数，得到平面应变方向上主应力计算公式的一个较合理形式，为应力状态和材料性质的函数。

The bilinear elastic-plastic constitutive relations of Zeolite sodalite and ferrierite crystals were gained from a number of finite element simulations using search method.

基于弹塑性双线性本构关系假定，用ANSYS有限元程序模拟纳米压痕实验过程，利用搜索法得到沸石大单晶SOD和FER的双线性本构关系。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新