Fast algorithms for designing variable FIR notch filters

The paper presents fast algorithms for designing finite impulse response (FIR) notch filters. The aim is to design a digital FIR notch filter so that the magnitude of the filter has a deep notch at a specified frequency, and as the notch frequency changes, the filter coefficients should be able to track the notch fast in real time. The filter design problem is first converted into a convex optimization problem in the autocorrelation domain. The frequency response of the autocorrelation of the filter impulse response is compared with the desired filter response and the integral square error is minimized with respect to the unknown autocorrelation coefficients. Spectral factorization is used to calculate the coefficients of the filter. In the optimization process, the computational advantage is obtained by exploiting the structure of the Hessian matrix which consists of a Toeplitz plus a Hankel matrix. Two methods have been used for solving the Toeplitz‐plus‐Hankel system of equations. In the first method, the computational time is reduced by using Block–Levinson's recursion for solving the Toeplitz‐plus‐Hankel system of matrices. In the second method, the conjugate gradient method with different preconditioners is used to solve the system. Comparative studies demonstrate the computational advantages of the latter. Both these algorithms have been used to obtain the autocorrelation coefficients of notch filters with different orders. The original filter coefficients are found by spectral factorization and each of these filters have been tested for filtering synthetic as well as real‐life signals. Copyright © 2007 John Wiley & Sons, Ltd.     

A comparative performance evaluation of micro-Raman spectrograph using holographic notch filter and dielectric filter

An indigenously designed and developed micro-Raman spectrograph, consisting of a diode-pumped solid-state green laser for the excitation of Raman scattering, a Raman imaging microscope, CCD as a detector and a notch filter, has been extensively studied to evaluate its performance. A dielectric edge filter (having 27 alternate layers of SiO₂ and TiO₂) and a holographic notch filter (Oriel make) have been used to block the Rayleigh scattered light from the sample to the entrance slit of the spectrograph. Holographic notch filter is found to be able to record the Raman shifts below 700 cm⁻¹ conveniently whereas dielectric edge filter (27 layers) has enabled the spectrograph to record the Raman spectra very efficiently after a wave-number shift of 700 cm⁻¹. It has also been observed that the instrument using the edge filter provides a peculiar spectrum consisting of three spectral lines having Raman shifts as 569, 1328 and 1393 cm⁻¹ in the Raman spectrum of a weakly scattering sample with large reflectivity. Similarly, a spectrum consisting of multiple lines has been observed when the instrument is being operated using a holographic notch filter. These spectral lines are not observed in the case of liquid samples such as benzene, carbon tetrachloride, ethanol, diethyl ether etc. The origin of these peculiar spectral lines has been briefly discussed in the paper. Additionally, a major motivation for this work is to utilize the results for the selection of an appropriate filter depending on the type of the sample, i.e. weakly scattered and highly reflecting sample or highly scattered and low reflecting sample.     

缺口根部和裂纹尖端残余应力的X射线法测定

X射线法用于缺口根部和裂纹尖端等徽区的残余应力测试的先决条件是解决缩小光束直径、提高衍射束的强度和准确设置试样等技术问题.在X射线衍射仪上借助于自行设计制造的限束对光装置和侧倾对中附件,成功地测定了缺口根部半径为1mm的喷丸残余应力场和板形试样压-压周期载荷下裂纹尖端的残余拉应力场.     

Construction of high-quality narrow-band holographic filters

We have studied the factors limiting the quality of holographic notch filters. We have employed a novel recording scheme in which the sample is translated during exposure, eliminating flare due to reflections at the boundaries, and simultaneously reducing the scatter of the final hologram. We have also refined a gravity-settling dichromated gelatine (DCG) deposition technique and incorporated hardening of the DCG layers during the drying stage. With this, we have produced high optical quality, uniform, flare-free DCG filters with an optical density, OD > 5, bandwidth < 20 nm and scatter almost as low as that for state of the art dielectric notch filters.     

On a Problem of Byrnes concerning Polynomials with Restricted Coefficients

We consider a question of Byrnes concerning the minimal degree of a polynomial with all coefficients in which has a zero of a given order at . For , we prove his conjecture that the monic polynomial of this type of minimal degree is given by , but we disprove this for . We prove that a polynomial of this type must have , which is in sharp contrast with the situation when one allows coefficients in . The proofs use simple number theoretic ideas and depend ultimately on the fact that .

     

基于快速傅里叶变换的条纹图像处理研究

为提高船体扭转角变形测量精度,对双光栅干涉测量法产生的莫尔条纹采用快速傅里叶变换频域处理。采集不同宽度的莫尔条纹图像,分别对图像进行快速傅里叶变换,对比分析图像频谱,得到实际莫尔条纹图像的有效频率信息。分析滤波器的选择原则,选用陷波低通滤波器,去除频域图像中高频噪声,获得莫尔条纹有效信息。实验结果表明,莫尔条纹的频域处理精度远高于空域处理结果,使扭转角测量精度提高到1.2″。     

Ⅰ-Ⅱ复合型尖V形切口脆断准则

基于最大周向应力和Seweryn-Novozhilov准则,用线弹性奇异应力场,给出Ⅰ-Ⅱ复合型尖V形切口的脆性断裂准则;并把裂纹作为切口张角为零的V形切口,这样就把V形切口问题与裂纹问题的断裂准则统一起来.为了验证该准则,本文采用有机玻璃板材加工多种V形切口试件进行了拉伸实验;同时,应用该准则对文献[16]中复合载荷下双边切口试件进行了起裂方向和临界载荷预测,并与其实验结果相比较.结果表明,本文所给出的Ⅰ-Ⅱ复合型尖V形切口脆性断裂准则与实验是相吻合的,适合于实际工程应用。     

开孔热塑性复合材料的三维弹塑性面内应力分析

本文利用一单参数三维塑性模型对AS4/PEEK热塑性复合材料的塑性行为进行表征。利用有限元程序生成系统FEPG,将复合材料的三维单参数塑性模型引入该系统中,编制了相应的有限元程序。通过将本文的有限元计算结果与文献实验结果进行对比,证明了所生成程序的精确性。并对AS4/PEEK热塑性复合材料层合板[0/90]s的面内应力进行了计算与分析。给出了0°层与90°层的面内应力。0°层的最大应力σx大约是90°层相应值的20倍,这主要是由于热塑性复合材料AS4/PEEK的纵向和横向模量存在很大的不同,并且具有明显的弹塑性行为所造成的。     

有限厚双边U型切口板的三维弹塑性有限元分析

针对单向拉伸载荷作用下的有限厚双边 U型切口板 ,本文对其切口根部的三维效应进行了详细的三维弹塑性大变形有限元分析 ,得到了不同于平面切口问题的新结果 :( 1 )在线弹性阶段 ,三维切口根部的应力集中因子 Kt高于二维情形 ,且 Kt在板厚 ( B)约为 8倍切口根部半径 (ρ)时达到峰值 ;进入塑性后 ,切口根部的 Kt随载荷水平的增加逐渐下降 ,并介于平面应力和平面应变情形之间 ;( 2 )切口前缘等效应变εe的最大值出现在约束最高的中面 ,且可比约束最低的自由表面处的应变值高一倍 ;( 3)薄板中 ,塑性区尺寸 xp 的最大值不是出现在约束较低的自由表面 ,而是出现在约束较高的中面 ,但随 B/ρ的增大逐渐向自由表面外推 ;( 4 )面内应力比 Tx在切口根部塑性区内的分布对板厚和载荷水平不敏感 ,可以用 Hill的滑移线解很好地近似。另外 ,对三维影响区内一些重要的三维约束参量进行了详细分析 ,总结了它们的三维分布规律。