理解Al—Mn—Si二十面体准晶的HREM图

提出了处理数字化图像的光滑算子。用它处理了Ａｌ－Ｍｎ－Ｓｉ二十面体准晶的高分辨电子显微图，处理后的图像展示了周期结构特征，由此建立了一个平面周期模型，其Ｆｏｕｒｉｅｒ变换图符合Ａｌ－Ｍｎ－Ｓｉ准晶相应的电子衍射图。     

Al—8Fe—3Ti急冷合金的组织稳定性

本文研究了Ａｌ－８Ｆｅ－３Ｔｉ急冷合金中的亚稳相结构及合金在退火过程中组织和性能的变化。结果表明：合金中存在ＡｌｍＦｅ，Ａｌ６Ｆｅ及“Ｖ”相，另外还有一种新发现的富Ｔｉ相，合金具有较高的热稳定性。     

Al—8Fe－3Ti急冷合金的组织稳定性

本文研究了Ａｌ－８Ｆｅ－３Ｔｉ急冷合金中的亚稳相结构及合金在退火过程中组织和性能的变化．结果表明：合金中存在ＡｌｍＦｅ、Ａｌ６Ｆｅ及“Ｖ”相，另外还有一种新发现的富Ｔｉ相。合金具有效高的热稳定性。     

非经典周期模型Fourier变换和群

本文提出３类具有局部８、１０和１２次对称的非经典平面周期格子，它们可被解释为相应的多面体所组成的空间模型在平面的投影，空间模型的Ｆｏｕｒｉｅｒ变换图显示出近似的８、１０和１２次旋转对称，但这些对称很难区别于相应的具有严格数学意义的旋转对称，并定性地相似于对应准晶的电子衍射图中显示的８、１０和１２次对称．利用传统的平移操作和旋转操作“合成”的新规则可描述非经典周期格，而这些合成操作本身构成了群，从而建立了非经典平晶体群。     

Fe-Mn-Al-C 合金相结构的经验判别公式

提出了γＢ相中Ｃ,Ａｌ,Ｍｎ元素含量的计算公式,以γＢ相为参照,得到了Ｆｅ－Ｍｎ－Ａｌ－Ｃ合金相结构唯一性判据的经验计算公式．     

Fe—Mn—Al—C合金相结构的经验判别公式

提出了γＢ相中Ｃ,Ａｌ,Ｍｎ元素含量的计算公式,以γＢ相为参照,得到了Ｆｅ－Ｍｎ－Ａｌ－Ｃ合金相结构唯一性判据的经验计算公式。     

Cr—Al复全钝化膜的组成及稳定性研究

本文在０．５ｍｏｌ／ＬＨ２ＳＯ４中测定了Ｆｅ－Ｃｒ，Ｆｅ－Ａｌ，Ｆｅ－Ｃｒ－Ａｌ和Ｆｅ－Ｍｎ－Ａｌ－Ｃｒ合金的极化曲线，用透射电镜和光电子能谱仪对它们的钝化膜的组成和稳定性进行了分析研究。结果表明：在上述合金的钝化膜中，均出现了Ｃｒ，Ａｌ的富集，但要Ｆｅ－Ｃｒ－Ａｌ合金的钝化膜中，Ｃｒ的富集受到抑制，而在Ｆｅ－Ｍｎ－Ａｌ－Ｃｒ合金的钝化膜中Ｃｒ富集未受到抑制。     

Cr-Al复合钝化膜的组成及稳定性研究

本文在０．５ｍｏｌ／ＬＨ２ＳＯ４中测定了Ｆｅ－Ｃｒ、Ｆｅ－Ａｌ、Ｆｅ－Ｃｒ－Ａｌ和Ｆｅ－Ｍｎ－Ａｌ－Ｃｒ合金的极化曲线，用透射电镜和光电子能谱仪对它们的钝化膜的组成和稳定性进行了分析研究．结果表明：在上述合金的钝化膜中，均出现Ｃｒ、Ａｌ的富集，但在Ｆｅ－Ｃｒ－Ａｌ合金的钝化膜中，Ｃｒ的富集受到抑制，而在Ｆｅ－Ｍｎ－Ａｌ－Ｃｒ合金的钝化膜中Ｃｒ富集未受到抑制．Ｆｅ－Ｍｎ－Ａｌ－Ｃｒ的Ｃｒ、Ａｌ复合钝化膜的钝性优于同等含Ｃｒ量的Ｆｅ－Ｃｒ合金，更优于同等Ｃｒ、Ａｌ含量的Ｆｅ－Ｃｒ－Ａｌ合金．本文认为，锰使得膜中的硫含量降低，致使钝化膜的稳定性提高     

Fe含量对Al—Fe合金加工软化的影响

研究了在纯铝（９９．９６％Ａｌ）中加入不同含量Ｆｅ的Ａｌ－Ｆｅ合金加工软化规律，结果表明：纯铝中加入２％Ｆｅ的Ａｌ－Ｆｅ合金，在轧制率达９０％以上时出现加工软化现象；多边化回复是加工软化的主要原因；第二相的存在有利于多边化回复。     

快速凝固 Al-Fe 合金中准晶相的研究

在快速凝固Ａｌ－Ｆｅ－Ｖ－Ｓｉ合金棒材中发现了１种圆形准晶相,尺寸为０２～０５μｍ,成分为Ａｌ－８０ａｔ％Ｆｅ－２．１ａｔ％Ｖ－３．２ａｔ％Ｓｉ。对此准晶进行了透射电镜、Ｘ－光衍射结构分析,并对准晶的形成机制进行了讨论。     

光栅光调制器周期结构的优化分析与实验

针对光栅光调制器的光学调制特点,建立一种可变周期结构的光栅光调制器模型,采用Matlab软件中的数字图像处理方法进行研究。利用傅里叶变换分析两种周期结构的光栅光调制器在频谱面和像面的光场分布,并得到不同周期结构对器件调制对比度的影响。实验得到了两种结构像面的光强输出对比。结果表明:不同周期结构对器件的亮态调制效果影响不大;当器件上下反射面中心对齐,下层反射面在器件周期方向两侧各超出上层光栅面的1/2倍光栅间隙宽度时,器件具有最佳的暗态调制效果,从而得到了光栅光调制器的一种周期结构优化方案。     

Multi-channel sampling theorems for band-limited signals with fractional Fourier transform

Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies. Supported partially by the National Natural Science Foundation of China (Grant Nos. 60232010 and 60572094) and the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104)     

Generalization of the Fourier transform-based method for calculating the response of a periodic railway track subject to a moving harmonic load

A Fourier transform-based method has been developed for calculating the response of a railway track as an infinitely long uniform periodic structure subject to moving or stationary harmonic loads. The track may become a non-uniform periodic structure by, for example, rail dampers which are installed between sleepers to control rolling noise and roughness growth. The period of the structure may become greater than the sleeper spacing. For those new situations, the current version of the method cannot be directly applied; it must be generalized and this is the aim of this paper. Generalization is performed by applying periodic conditions to each type of support and summarizing contributions from all types of support. Responses of the rail, sleeper, and damper are all formulated as an inverse Fourier transform from wavenumber domain to spatial domain. The generalized method is applied to investigate dynamics of a typical track with rail dampers of particular design. It is found that the rail dampers can significantly suppress the pinned–pinned vibration of the original track, widen the stop bands and increase vibration decay rate along the rail. However, it is also found that a new pinned–pinned mode is created by the dampers and between about 450 and 1,300 Hz dampers vibrate stronger than the rail, making noise radiation from the dampers a potential issue. These concerns must be fully investigated in the future. The formulae presented in this paper provide a powerful tool to do that.

     

函数拟合连续信号的频谱分析

用插值函数拟合代替抽样函数求有限长连续信号和周期信号的频谱 ,推导出用离散信号傅里叶变换公式求拟合连续信号频谱的方法 ,该方法能用离散傅里叶变换的公式更准确地求出连续信号的频谱 .该方法可以非常方便地改进现有信号分析仪性能价格比     

改进的双速率同步采样法及其傅里叶变换

针对现有的双速率同步采样序列离散傅里叶变换(DFT)的算法是一个经验公式和计算量大的缺陷,提出了一种改进的双速率同步采样法.改进的采样法采用传统的采样间隔补偿方法以平抑对周期信号采样所产生的周期误差,将所有的采样点按时间顺序划分成点数相同的前后两组,对两段中对应点的采样间隔分别给以相同的补偿,将双速率采样问题归结成均匀采样问题,并利用均匀采样的基本理论,导出改进的双速率采样序列DFT的算法.分析结果表明,与传统补偿方法相比,改进的采样法不仅能有效地抑制采样的周期误差,而且DFT算法的乘法计算量减少了一半.适用于周期信号的电参数测量与频谱分析.     

M序列的对称性变换及对称群

n级M序列是由n级非线性回馈移位寄存器产生的周期为2n的二元序列,也称为de Bruijn序列。该文将讨论M序列的对称性变换,提出了一类新的对称性变换——"与/或"逻辑对称性变换,并研究了基于对称性变换的对称群。     

模拟傅立叶变换技术在伪随机多频观测系统中的应用

2n系列伪随机多频信号是一种较为有效的地球物理激励场源。通过对任意周期信号数学表达式的分析,伪随机多频信号中某一频率信号的幅度与相位可由类似傅立叶变换的表达式求得。在此基础上,设计了相应的硬件电路来实现模拟信号的傅立叶变换,实现对伪随机多频观测系统中的信号幅度和相位观测。硬件电路主要由信号发生器、乘法器和积分器等集成芯片器件组成,简单实用。实验结果表明该技术有良好观测精度,抗干扰能力强,能有效地进行伪随机多频信号观测。     

关于特殊周期序列的线性复杂度的研究

综述了具有特殊周期序列的线性复杂度的研究途径、现状和方向,分析了以Ｍａｓｓｅｙ引入的广义离散傅里叶变换作为研究工具取得的最新结果,特别指出了该方向上几个值得研究的问题及方向     

双曲对称中的分形集

目的将分形集通过双曲变换压缩入双曲极限圆中,构造具有分形特性的极限圆图案.方法分析双曲对称群的特点,改造欧式平面上构造经典分形的IFS迭代函数系,利用这种迭代函数系与双曲平面对称变换构造出组合IFS,通过随机挑选组合IFS中的仿射变换,构造双曲排列的分形集.结果实现了将欧式平面的经典分形集以及普通的汉字压缩到了双曲平面上.结论笔者所提出的构造技术可以用于生成包含经典分形的双曲对称图案以及双曲对称排列的汉字艺术图案.     

Filterbank implementation for multi-channel sampling in fractional Fourier domain

Reconstruction of a continuous time signal from its periodic nonuniform samples and multi-channel samples is fundamental for multi-channel parallel A/D and MIMO systems. In this paper, with a filterbank interpretation of sampling schemes, the efficient interpolation and reconstruction methods for periodic nonuniform sampling and multi-channel sampling in the fractional Fourier domain are presented. Firstly, the interpolation and sampling identities in the fractional Fourier domain are derived by the properties of the fractional Fourier transform. Then, the particularly efficient filterbank implementations for the periodic nonuniform sampling and the multi-channel sampling in the fractional Fourier domain are introduced. At last, the relationship between the multi-channel sampling and the filterbank in the fractional Fourier domain is investigated, which shows that any perfect reconstruction filterbank can lead to new sampling and reconstruction strategies. Supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104), the National Natural Science Foundation of China (Grant Nos. 60890072, 60572094) and the National Key Basic Research Program Founded by MOST (Grant No. 2009CB724003)