A discrete fractional random transform
基于某分数阶傅里叶变换地chirp信号全参数估计及代码
摘要线性调频信号即LFM信号是一种在雷达，通信，声纳，地震探测等领域中有着重要作用的非平稳信号。
因为LFM信号是一种非平稳信号，对它进行参数估计会比较复杂，现在的处理方法大多是使用时频面上的二维峰值搜索。
分数阶傅里叶变换是时频变换中的一种，因为它在处理多分量LFM信号时不会产生交叉项，所以在LFM信号的参数估计中得到了广泛的应用。
本文首先介绍了分数阶傅里叶变换的基本定义及性质，然后介绍了变换的离散算法中的采样型算法，即Ozaktas采样型算法和Pei采样型算法，并使用这两种算法在matlab上进行了LFM信号参数估计的仿真实验。
在论文的安排上，首先介绍了题目的背景和所做的工作；然后，介绍了离散分数阶傅里叶变换的定义及计算过程，还有使用这些算法进行参数估计时的计算方法；之后，讲述了的仿真过程和结果；最后，对实验结果进行了分析和主观评估。
关键词：分数阶傅里叶变换；线性调频信号；参数估计；离散算法AbstractThe LFM signal is a kind of non-stationary signal ,which plays an important role in the field of radar, communication, sonar, seismic detection etc.Because of LFM signal is a nonstationary signal, so the parameter estimation for it is more complex. now most of the method to estimation it parameter,is two-dimensional peak search on ime-frequency plane .Fractional Fourier transform is one kind of frequency conversion, because when it's processing the multi-component LFM signal it will not get cross terms. so it has been widely used in the parameter estimation of LFM signal .This article first introduces tthen introduces the discrete fractional Fourier transform algorithm type of sampling algorithm, and use these two kinds of algorithm do parameter estimation of LFM signal simulation experiment on matlab.On the arrangement of the thesis, the author firstly introduces the background of the topic and the authors have done;Then, this paper introduces the definition of discrete fractional Fourier transform and the calculation process, and using these algorithms for parameter estimation method;After, tells the way of the process and results of the author;Finally, the experimental results are analyzed and subjective evaluation.Keywords: FRFT；LFM signal；parameter estimation；disperse calculate目录第1章引言 (1)1.1 应用背景及其意义 (1)1.2 研究的现状 (2)第2章离散分数阶傅里叶变换 (7)2.1 分数阶傅里叶变换 (7)2.1.1 分数阶傅里叶变换的定义 (7)2.1.2 分数阶傅里叶变换的性质 (9)2.2 离散分数阶傅里叶变换 (11)2.2.1 离散分数阶傅里叶变换简介 (11)2.2.2 Ozaktas采样型算法 (12)2.2.3 Pei采样型算法 (16)2.3 基于FRFT的LFM信号参数估计的理论模型 (18)2.3.1 基于Ozaktas算法的参数估计模型 (19)2.3.2 基于Pei算法的参数估计模型 (21)第三章基于DFRFT的LFM信号参数估计 (22)3.1 引言 (22)3.1.1主要技术和方法 (22)3.1.2问题总结与分析 (23)3.2 算法设计及实验分析 (24)3.2.1 使用FFT来对LFM信号进行参数估计 (24)3.2.2 基于Ozaktas算法的参数估计 (27)3.2.3 基于Pei算法的参数估计 (31)第4章对实验结果的分析 (39)4.1两种算法对参数估计的实验结果分析 (39)4.2仿真程序的展示界面 (40)第5章总结与展望 (43)致 (44)参考文献 (45)第1章引言1.1 应用背景及其意义LFM信号是时变信号中的一种的典型代表，线性调频信号（LFM信号）[1]可以说是无所不在的。
数学词汇英文翻译
数学专业词汇Aabsolute value 绝对值 accept 接受 acceptable region 接受域additivity 可加性 adjusted 调整的 alternative hypothesis 对立假设analysis 分析 analysis of covariance 协方差分析 analysis of variance 方差分析 arithmetic mean 算术平均值 association 相关性 assumption 假设 assumption checking 假设检验 availability 有效度average 均值Bbalanced 平衡的 band 带宽 bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算 case 个案 category 类别 center of gravity 重心 central tendency 中心趋势 chi-square distribution 卡方分布 chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较 comparison 对照 components 构成，分量 compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量 control charts 控制图 correlation 相关covariance 协方差 covariance matrix 协方差矩阵 critical point 临界点critical value 临界值 crosstab 列联表cubic 三次的，立方的 cubic term 三次项 cumulative distribution function 累加分布函数 curve estimation 曲线估计Ddata 数据 default 默认的 definition 定义 deleted residual 剔除残差density function 密度函数 dependent variable 因变量 description 描述design of experiment 试验设计 deviations 差异 df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离 distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值 equal size 等含量 equation 方程 error 误差 estimate 估计 estimation of parameters 参数估计 estimations 估计量 evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的 exponential distributon 指数分布 extreme value 极值 F factor 因素，因子 factor analysis 因子分析 factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线 fitted value 拟合值 fixed model 固定模型 fixed variable 固定变量 fractional factorial design 部分析因设计 frequency 频数 F-test F检验 full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布 geometric mean 几何均值 group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立 independent variable 自变量independent-samples 独立样本 index 指数 index of correlation 相关指数 interaction 交互作用interclass correlation 组内相关 interval estimate 区间估计 intraclass correlation 组间相关 inverse 倒数的iterate 迭代Kkernal 核 Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验 kurtosis 峰度Llarge sample problem 大样本问题 layer 层least-significant difference 最小显著差数 least-square estimation 最小二乘估计 least-square method 最小二乘法 level 水平 level of significance 显著性水平 leverage value 中心化杠杆值 life 寿命 life test 寿命试验 likelihood function 似然函数likelihood ratio test 似然比检验 linear 线性的 linear estimator 线性估计linear model 线性模型 linear regression 线性回归 linear relation 线性关系 linear term 线性项 logarithmic 对数的 logarithms 对数 logistic 逻辑的 lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估计 mean squared deviation(MSD) 均方差 mean sum of square 均方和 measure 衡量 media 中位数 M-estimator M估计minimum 最小值 missing values 缺失值 mixed model 混合模型 mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程multiple response 多响应 multivariate analysis 多元分析Nnegative relationship 负相关 nonadditively 不可加性 nonlinear 非线性nonlinear regression 非线性回归 noparametric tests 非参数检验 normal distribution 正态分布 null hypothesis 零假设 number of cases 个案数Oone-sample 单样本 one-tailed test 单侧检验 one-way ANOVA 单向方差分析one-way classification 单向分类 optimal 优化的optimum allocation 最优配制 order 排序order statistics 次序统计量 origin 原点orthogonal 正交的 outliers 异常值Ppaired observations 成对观测数据 paired-sample 成对样本 parameter 参数parameter estimation 参数估计 partial correlation 偏相关partial correlation coefficient 偏相关系数 partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估计 poisson distribution 泊松分布 polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关 power 幂P-P plot P-P概率图 predict 预测 predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析 proability 概率 probability density function 概率密度函数 probit analysis 概率分析 proportion 比例Qqadratic 二次的 Q-Q plot Q-Q概率图quadratic term 二次项 quality control 质量控制 quantitative 数量的，度量的 quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样 random seed 随机数种子 random variable 随机变量randomization 随机化 range 极差 rank 秩 rank correlation 秩相关 rank statistic 秩统计量 regression analysis 回归分析 regression coefficient 回归系数 regression line 回归线 reject 拒绝 rejection region 拒绝域relationship 关系 reliability 可*性 repeated 重复的 report 报告，报表residual 残差 residual sum of squares 剩余平方和 response 响应 risk function 风险函数 robustness 稳健性 root mean square 标准差 row 行 run 游程 run test 游程检验Sample 样本 sample size 样本容量 sample space 样本空间 sampling 取样sampling inspection 抽样检验 scatter chart 散点图 S-curve S形曲线separately 单独地 sets 集合 sign test 符号检验 significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布 skewness 偏度 small sample problem 小样本问题smooth 平滑 sort 排序 soruces of variation 方差来源 space 空间 spread 扩展 square 平方 standard deviation 标准离差 standard error of mean 均值的标准误差 standardization 标准化 standardize 标准化 statistic 统计量 statistical quality control 统计质量控制 std. residual 标准残差stepwise regression analysis 逐步回归 stimulus 刺激 strong assumption 强假设 stud. deleted residual 学生化剔除残差 stud. residual 学生化残差subsamples 次级样本sufficient statistic 充分统计量 sum 和 sum of squares 平方和 summary 概括，综述Ttable 表 t-distribution t分布 test 检验 test criterion 检验判据 test for linearity 线性检验 test of goodness of fit 拟合优度检验 test of homogeneity 齐性检验 test of independence 独立性检验 test rules 检验法则 test statistics 检验统计量 testing function 检验函数 time series 时间序列tolerance limits 容许限total 总共，和 transformation 转换treatment 处理 trimmed mean 截尾均值 true value 真值 t-test t检验two-tailed test 双侧检验Uunbalanced 不平衡的 unbiased estimation 无偏估计 unbiasedness 无偏性uniform distribution 均匀分布Vvalue of estimator 估计值variable 变量variance 方差variance components 方差分量 variance ratio 方差比 various 不同的 vector 向量Wweight 加权，权重 weighted average 加权平均值 within groups 组内的ZZ score Z分数2. 最优化方法词汇英汉对照表Aactive constraint 活动约束 active set method 活动集法 analytic gradient 解析梯度 approximate 近似 arbitrary 强制性的 argument 变量 attainment factor 达到因子Bbandwidth 带宽 be equivalent to 等价于 best-fit 最佳拟合 bound 边界Ccoefficient 系数 complex-value 复数值 component 分量 constant 常数constrained 有约束的constraint 约束constraint function 约束函数continuous 连续的 converge 收敛 cubic polynomial interpolation method 三次多项式插值法 curve-fitting 曲线拟合Ddata-fitting 数据拟合 default 默认的，默认的 define 定义 diagonal 对角的direct search method 直接搜索法direction of search 搜索方向discontinuous 不连续Eeigenvalue 特征值 empty matrix 空矩阵 equality 等式 exceeded 溢出的Ffeasible 可行的 feasible solution 可行解 finite-difference 有限差分first-order 一阶GGauss-Newton method 高斯-牛顿法 goal attainment problem 目标达到问题gradient 梯度 gradient method 梯度法Hhandle 句柄 Hessian matrix 海色矩阵Independent variables 独立变量 inequality 不等式 infeasibility 不可行性 infeasible 不可行的 initial feasible solution 初始可行解 initialize 初始化 inverse 逆 invoke 激活 iteration 迭代 iteration 迭代JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子 large-scale 大型的 least square 最小二乘 least squares sense 最小二乘意义上的 Levenberg-Marquardt method 列文伯格-马夸尔特法 line search 一维搜索 linear 线性的 linear equality constraints 线性等式约束 linear programming problem 线性规划问题 local solution 局部解M medium-scale 中型的 minimize 最小化 mixed quadratic and cubic polynomial interpolation and extrapolation method 混合二次、三次多项式内插、外插法 multiobjective 多目标的Nnonlinear 非线性的 norm 范数Oobjective function 目标函数observed data 测量数据optimization routine 优化过程optimize 优化optimizer 求解器over-determined system 超定系统Pparameter 参数partial derivatives 偏导数polynomial interpolation method 多项式插值法Qquadratic 二次的 quadratic interpolation method 二次内插法 quadratic programming 二次规划Rreal-value 实数值 residuals 残差 robust 稳健的 robustness 稳健性，鲁棒性S scalar 标量 semi-infinitely problem 半无限问题 Sequential Quadratic Programming method 序列二次规划法simplex search method 单纯形法solution 解 sparse matrix 稀疏矩阵 sparsity pattern 稀疏模式 sparsity structure 稀疏结构 starting point 初始点 step length 步长 subspace trust region method 子空间置信域法 sum-of-squares 平方和 symmetric matrix 对称矩阵Ttermination message 终止信息 termination tolerance 终止容限 the exit condition 退出条件 the method of steepest descent 最速下降法 transpose 转置Uunconstrained 无约束的 under-determined system 负定系统Vvariable 变量 vector 矢量Wweighting matrix 加权矩阵3 样条词汇英汉对照表Aapproximation 逼近 array 数组 a spline in b-form/b-spline b样条 a spline of polynomial piece /ppform spline 分段多项式样条Bbivariate spline function 二元样条函数 break/breaks 断点Ccoefficient/coefficients 系数 cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式 cubic smoothing spline 三次平滑样条 cubic spline 三次样条 cubic spline interpolation 三次样条插值/三次样条内插curve 曲线Ddegree of freedom 自由度 dimension 维数Eend conditions 约束条件 input argument 输入参数 interpolation 插值/内插 interval 取值区间Kknot/knots 节点Lleast-squares approximation 最小二乘拟合Mmultiplicity 重次 multivariate function 多元函数Ooptional argument 可选参数 order 阶次 output argument 输出参数P point/points 数据点Rrational spline 有理样条 rounding error 舍入误差（相对误差）Sscalar 标量 sequence 数列（数组） spline 样条 spline approximation 样条逼近/样条拟合spline function 样条函数 spline curve 样条曲线 spline interpolation 样条插值/样条内插spline surface 样条曲面 smoothing spline 平滑样条Ttolerance 允许精度Uunivariate function 一元函数Vvector 向量Wweight/weights 权重4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差 absolute tolerance 绝对容限 adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图 converge 收敛 coordinate 坐标系Ddecomposed 分解的 decomposed geometry matrix 分解几何矩阵 diagonal matrix 对角矩阵 Dirichlet boundary conditions Dirichlet边界条件Eeigenvalue 特征值 elliptic 椭圆形的error estimate 误差估计 exact solution 精确解Ggeneralized Neumann boundary condition 推广的Neumann边界条件 geometry 几何形状 geometry description matrix 几何描述矩阵 geometry matrix 几何矩阵 graphical user interface（GUI）图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子 Laplace equation 拉普拉斯方程 linear interpolation 线性插值 loop 循环Mmachine precision 机器精度 mixed boundary condition 混合边界条件NNeuman boundary condition Neuman边界条件 node point 节点 nonlinear solver 非线性求解器 normal vector 法向量PParabolic 抛物线型的 partial differential equation 偏微分方程 plane strain 平面应变plane stress 平面应力Poisson's equation 泊松方程polygon 多边形 positive definite 正定Qquality 质量Rrefined triangular mesh 加密的三角形网格 relative tolerance 相对容限relative tolerance 相对容限 residual 残差 residual norm 残差范数Ssingular 奇异的。
电气控制设备英语词汇
1、电气与控制技术load test and short-circuit test 负载试验〔短路试验〕plugging 反接制动与反向intermittent periodic duty 反复短时工作制feedback control 反响控制feedback loop 反响回路luminous intensity 发光强度distributed capacitance 分布电容split phase motor 分相电动机fractional horsepower motor 分马力电动机nonlinear control system 非线性控制系统nonlinear (circuit) element 非线性〔电路〕元件nonlinearity 非线性second class load 二级负荷rated condition 额定工况rated value 额定值short-time duty 短时工作制short circuit current 短路电流short circuit 短路series resonance 串联谐振transducer 传感器〔变换器〕magnetic core 磁心magnetization curve 磁化曲线magnetic field 磁场magnetic field strength 磁场强度magnetic saturation 磁饱和magnetic hysteresis loop 磁滞回线magnetic flux 磁通量magnetic flux density 磁通密度superconductor 超导体uninterrupted duty 持久工作制programmed control 程序控制stepping motor 步进电动机parallel resonance 并联谐振differentiation protection 差动庇护tachogenerator 测速发电机protective circuit 庇护电路open loop control 闭环控制apparent power 表示功率comparator 比较器nominal value 标称值speed governing by frequency convertion 变频调速speed governing by pole changing 变极调速ampere-turns 安匝safety voltage 安然电压semiconductor devices 半导体器件thyristor 半导体开关元件semiconductor 半导体(absolute)magnetic permeability 〔绝对〕磁导率current rating (of cable) [电缆的]载流量breaking capacity (of a switching device or a fuse〕[开关电器的或熔断器的]分断能力auxiliary circuit(of a switching device) [开关电器的]辅助电路alternating component (of a pulsating voltage or current〕[脉动电压或电流的]交流分量direct component〔of a pulsating voltage or current〕脉动电压或电流的]直流分量TTL circuitPI TTL电路PI regulatorPID 调节器PID regulatorPD 调节器PD regulator 调节器main circuit 主电路neutral point 中性点medium frequency 中频active power 有功功率active element 有源元件first class load 一级负荷hard magnetic material 硬磁材料direct control 直接控制direct coupling 直接耦合remote control 遥控sine wave 正弦波rectiffication 整流illuminance 照度operational amplifier 运算放大器load rate 用电负荷率piezoelectric effect 压电效应selector 选择器oxidation stability 氧化不变性couplingMOS 耦合MOS circuit 电路linear control system 线性控制系统linear(circuit)element 线性〔电路〕元件linearity 线性gas protection 瓦斯庇护reactive power 无功功率passive element 无源元件eddy current 涡流synchronous speed 同步转速on-load factor 通电持续率micromotor 微电机differentiator 微分电路regulated power supply 稳压电源voltage stabilizing circuit 稳压电路sequential order of the phases,phase sequence 相序phase 相位〔位相，相角〕phase displacement 相位移temperature rise 温升connection diagram of windings 绕组联结圈winding 绕组servo system 随动系统detuning 掉调distortion 掉真digital integrated circuit 数字集成电路digital display 数字显示digital quantity 数字量capacitive reactance 容抗third class load 三级负荷three-phase and three-wire sysyem 三相三线制three-phase and four-wire system 三相四线制soft magnetic material 软磁材料thermo-electric effect 热电效应thermal stability 热不变性thermistor 热敏电阻servomotor 伺服电动机servo mechanism 伺服机构output 输出input 输入flashover,arc-over 闪络D filp flop D触发器DTL circuit DTL电路logic circuit 逻辑电路excitation 励磁〔激磁〕contravariant 逆变bus,busbar 母线〔汇流排〕continuous control 持续控制continuous system 持续系统interlock 连锁connection symbol 联结组标号torque motor 力矩电动机analog quantity 模拟量potential drop of internal resistance 内阻压降whirling speeds 临界转速full load 满载pulsating current 脉动电流pulsating voltage 脉动电压pulser,pulse generator 脉冲发生器puncture test 耐压试验ideal inductor 抱负电感器ideal resistor 抱负电阻器ideal voltage source 抱负电压源ideal capacitor 抱负电容器ideal current source 抱负电流源ideal amplifier 抱负放大器ideal transformer 抱负变压器temperature classification,thermal stability classification 耐热等级filtering,filtration 滤波discrete system 离散系统zero-sequence protection 零序庇护load,charge 负载〔负荷〕inductosyn 感应同步器induced voltage 感应电压inductive reactance 感抗high frepuency 高频photoelectric effect 光电效应overcurrent protection 过电流庇护overvoltage protection 过电压庇护mains frequency 工频power factor 功率因数constant control system 恒值控制系统phasing 核相〔定相〕glow discharge 辉光放电fundamental wave 基波integrator 积分电路mutual induction 互感应commutation 换向change-over switching 换接parasitic capacitance 寄生电容detector 检测装置relay protection 继电庇护skin effect 集肤效应coercive force 矫顽力demodulation 解调dielectric loss 介质损耗contact voltage 接触电压contact resistance 接触电阻earth fault 接地故障ground device 接地装置resistance of an earthed conductor,earthing resistance 接地电阻cut-off 截止partial discharge 局部放电insulation resistance 绝缘电阻absorptance(absorption ratio) of insulation resistance 绝缘电阻的吸收比step vlotage 跨步电压programmable logic controllers 可编程序控制器no-load test 空载试验noload operation 空载运行open-circuit voltage 开路电压open loop control 开环控制diamagnetism 抗磁性control circuit 控制电器shielded cable 屏蔽电缆gas chromatograph test 气相色谱试验gas conduction 气体导电air gap 气隙signal circuit 信号电路small-power motor 小功率电动机resonance 谐振harmonic 谐波impedance 阻抗optimum control 最优控制autonomous control 自治调节synchro,selsyn 自整角机automatic reclosing equipment 自动重合闸automatic protection device 自动庇护装置automatic control 自动控制automatic control system 自动控制系统automatic regulating system 自动调节系统slip 转差率electric circuit 电路electric current 电流bridge 电桥armature reaction 电枢反响voltage,electric potential difference 电压〔电位差〕electric corona,corona,corona discharge 电晕〔放电〕power supply 电源electric field 电场electromagnetic wave 电磁波electromagnetic induction 电磁感应electromotive force 电动势inductor 电感线圈electric arc 电弧electric spark 电火花electrolytic corrosion 电解腐蚀dielectric 电介质reactance 电抗clearance 电气间隙electronic approach switch 电子接近开关conductance 电导equivalent electric circuit 等效电路earth,ground 地speed regulation,speed governing 调速speed governing system 调速系统range of speed regulation 调速范围speed governing by voltage regulation 调压调速modulation 调制amplitude modulation 调幅frequency modulation 调频2、IEC试验室产物Abrasion test 磨损测试设备Apparatus for burning test (vertical and horizontal) 程度垂直燃烧测试设备Apparatus for production testing of hand tools for live working 手动测试东西Apparatus for winding a flexible pipe 软管弯折试验设备Appliance couplers test equipment (various) 各类测试连接器Automatic & manual production test equipment - for final control 自动/手动产物测试设备- 出厂控制Ball-pressure test apparatus 球压测试装置Bending equipment for conduits 管路弯折设备Bump test 冲击测试Burning test, horiz. 燃烧测试〔程度〕Cable test apparatus (various) 各类线缆测试Draining current measuring equipment 损耗电流测试设备Drip proof test(special) 淋浴测试Drop test 跌落测试Dust chamber 防尘箱Dynamometers 功率计Earth bond resistance tester Earthing resistance test appliance 接地电阻测试设备Electric resistance of non-metallic materials 非金属材料的电阻测试Gauges and similar mechanical checking devices 量规或类似测试装置Electrode arrangements 测试电极装置Flexing test equipment 弯折试验Fume cupboard (protective cabinet) 防护罩Flexing test apparatus for cables 线缆弯折试验装置Flame hoods 燃烧罩Endurance test appliance for plugs 插头寿命测试Equipment for testing refrigerators 冰箱测试设备Endurance test appliance 寿命测试Gauges for appliance inlets Gauges for finished lamps 灯具量规Gauges for lampholders 灯座量规Hot wire ignition test 热丝引燃测试Hipot testers Hot mandrel test apparatus 高压机High voltage test appliance 耐压测试High frequency spark generator 高频火花发生器High current transformers 高电流变送器High current arc ignition test 大电流起弧测试Heating tests 高温测试Heating cabinets 高温试验箱Hand held shower 手持花洒Ground continuity testers 接地电阻测试Gauges for plugs and sockets 插头插座量规Humidity chambers 横湿箱Gauges for starters 策动机量规Impact balls 冲击球Glass vessel for microwave oven testing 微波炉测试的玻璃容器Impact hammers 冲击锤Glow-wire test apparatus 灼热丝测试设备Impact weight apparatus Inductive loads 电感负载Jet nozzles 喷嘴Lampholder testing apparatus (various) 各类灯座测试设备Kit bunsen burner/ needle flame test 燃烧测试套件〔本申/ 针焰〕Leakage current test appliance 泄露电流测试设备Laboratory power supply with isolation and regulation 可控别离尝试室电源Loading weights (various) 各类负重Laboratory stablized power supply unit 稳压源Luminaries testing equipment (various) 照明测试设备Measuring equipment for testing switches and socket-outlets (with DPM) 测试开关和插头插座测试设备Megohmeter 兆欧表Mechanical resistance testing apparatus for el. Irons Mechanismus for burning tests (vert. And horiz.) 程度或垂直燃烧机架Needle flame burners 针焰燃烧东西Needle flame miniature burner 微型针焰燃烧东西Surge test circuit 浪涌测试Needle flame tester 针焰测试Resistance loads 电阻负载Scratch test equipment 刮擦测试设备Power sources 电源Probe for measuring surface temperature 外表温度探头Pendulum hammer 摆锤Plugs for endurance tests of socket-outlets 插头插座寿命测试Needle flame thermometer 针焰温度表Plugs and socket test equipment (various) 各类插头插座设备Splash testing apparatus 溅水测试Pendulum impact test apparatus 摆锤冲击测试Spray apparatus, tubes 喷水测试Solderability test apparatus 可焊性的测试设备Standard test enclosure 尺度测试附件Temperature during operation, measuring equipment 温度测试Thermocouples 热电偶Temperature measurement 温度测试Test apparatus for IP tests IP 测试Torque test equipment 扭力测试Test finger nail 测试指甲Test panes for hob elements 燃气炉测试盘Test fingers 测试指Torsion apparatus 扭转测试Test hook 测试钩Tracking index apparatus 漏电起痕测试仪Test knifes 测试刀模Water evaporator 水蒸发器Test pin 测试真Tumbling barrel 滚筒试验装置Test probe 测试探头Variacs Vessel for testing induction hotplates 测试热传导的容器3、设备补缀corrective maintenance 改善补缀back repair rate 返修率stepped(sizing) repair 分级补缀decentralized maintenance system 分散补缀制waste and ungraded product and back repair loss 废次品及返修损掉unscheduled maintenance time 非预定维修时间periodic repair task 按期补缀作业periodic repair 按期维修法location accuracy 定位精度transmission accuracy 传动精度revision of overhaul plan 大修方案点窜assesment of overhaul plan 大修方案查核overhaul planning 大修方案编制basis of overhaul plan 大修方案依据fulfilment rate of overhaul plan 大修方案完成率implementation of overhaul plan 大修方案实施overhaul cost 大修费用overhaul cost 大修成本构成overhaul cost analysis 大修成本阐发fulfilment rate of overhaul cost 大修成本完成率overhaul guarantee 大修保修interval between overhauls, overhaul cycle 大修周期guarantee system of overhaul quality 大修质量包管体系overhaul quality evaluation 大补缀质量评定overhaul quality control 大补缀质量控制overhaul,capital repair 大修assembly repair 部件补缀法partial repair 局部补缀法compensation method 抵偿法production program of spqre parts 备件出产方案stand-by or redundancy system 备份或冗余系统standard-size repair method 尺度尺寸补缀法“eight steps〞method 八步法repeat location accuracy 重复定位精度middle repair 中修system with maintainable standby parts 有可维修备份的系统remote maintenance 远距离维修preventive maintenance 预防维修scheduled maintenance time 预定维修时间predictive maintenance 预知维修〔状态监测维修〕quality system 质量体系quality 质量deferred maintenance 逾期维修network planning 网络方案maintenance skill training 维修技术培训maintenance interval, uptime 维修间隔〔正常运行时间〕economic analysis of maintenance activities 维修活动的经济阐发maintenance worker 维修工人maintenance protection 维修防护maintenance shop 维修车间maintenance prevention 维修预防maintenance cycle 维修周期maintenance time 维修时间synchronous repair 同步补缀法repair downtime 停修时间item repair 项修〔工程补缀〕repair on commission 外委补缀〔TPM〕total production maintenance system 全员参加的出产维修制controlled maintenance 受控维修life cycle maintenance 寿命周期维修hot repair 热修repair schedule of equipment 设备补缀方案acceptance check for equipment repair 设备补缀验收quarterly repair schedule of equipment 设备季度补缀方案technical check of equipment 设备技术查核equipment overhaul plan 设备大修方案monthly repair schedule of equipment 设备月度补缀方案equipment maintenance plan 设备维修方案three essential factors of equipment maintenance 设备维修三要素item repair plan of equipment 设备项修方案annual repair schedule of equipment 设备年度补缀方案breakdown maintenance 事后补缀first-aid repair 抢修accuracy of machine tool after overhaul 大修机床精度rolling (circulation) plan 滚动方案MIS maintenance 办理信息系统维修process capacity index 工程能力指数working accuracy 工作精度recovery repair 恢复性补缀rotational accuracy of machine tool 机床旋转精度machine repair shop 机修车间〔分厂〕maintenance mechanic 机修技工mechanical repair method 机械修复法instantaneous efficiency of machinery 机械的瞬时效率interchange method 互换法inspection 查验centralized maintenance system 集中补缀制geometric accuracy 几何精度seasonal repair 季节性补缀repair out of plan 方案外补缀scheduled maintenance 方案维修planned preventive maintenance system 方案预修制planned repair 方案补缀contact accuracy 接触精度emergency repair task 紧急补缀作业machining and fitting method on the spot 当场加工修配法precision index 精度指数accuracy standard 精度尺度precision retaining ability 精度保持性precision reserve 精度储藏fine repair 精修fine repair mechanic 精修技工economic accuracy 经济精度balancing precision grade 平衡精度等级mean time to repair(MTTR), mean repair time 平均补缀时间minor repair 小修fitting method 修配法repair link 修配环repair specification 补缀任务书repair rasks dispatch 补缀施工调剂repair time, shutdown time 补缀时间downtime quota for equipment repair 补缀停歇时间定额repair facilities 补缀用设备repair quality 补缀质量repair quality index 补缀质量指标repair quality plan 补缀质量方案repair quality assessment 补缀质量查核repair symbols 补缀标识repair cost assessment 补缀成本查核repair size 补缀尺寸repair quota 补缀定额repair cost quota 补缀费用定额repair scheme 补缀方案repair manhour quota 补缀工时定额repair manhours assessment 补缀工时查核repair technology 补缀工艺maintenance engineering truck 补缀工程车maintenance tool 补缀东西repair time limit assessment 补缀工期查核repair assessment 补缀查核inspection before repair 修前预检measuring and drawing before repair 修前测绘inquiry before repair 修前拜候service after repair 修后效劳optimum repair cycle 最优补缀周期assembly accuracy 装配精度electric repair shop 电修车间〔分厂〕maintenance electrician 电修技工repair cost accounting for single equipment 单台设备补缀费用核算adjustment method 调整法adjusting link 调整环4、设备办理probability 概率〔几率〕variance 方差decentralized maintenance 分散维修dynamic test 动态试验power facilities management 动力设备设施办理duct-proof and protective equipment management 除尘、防护设备办理sampling investigation 抽样查询拜访domestic production management of imported spare parts 备件国产化办理standard deviation 尺度偏差budget of installation 安装预算machine contracting system 包机制regulation of check and lubrication before on shift 班前查抄与润滑制度shift relief system ［设备］交接班制度Equipment Management Regulation 设备办理条例〔条例〕repair [设备]补缀maintenance (and repair) [设备]维修key-point investigation 重点查询拜访management of key-point equipment 重点设备办理key-point equipment 重点设备liability accident 责任变乱exponential distribution 指数分布histogram 直方图prepayment and collection 预付与托收承付prophylactic test 预防性试验prevention first 预防为主orthogonal design 正交设计法〔正交试验法〕normal distribution 正态分布transportation vehicle management system 运输车辆办理制度three guarantees of quality 质量“三包〞accident due to quality 质量变乱management regulation of pressure vessel 压力容器办理制度mean time to failure 无故障运行时间Weibull distribution 威布尔分布idle equipment management 闲置设备办理制度idle plant 闲置设备statistical analysis 统计阐发maintainability 维修性maintenance information management 维修信息办理combination of service and planned maintenance 维护与方案检修相结合random event 随机事件numerical control (NC) equipment management 数控设备办理three-level service system 三级调养制mathematical expectation 数学期望mathematical model 数学模型mathematical statistics 数理统计technical facilities in production 出产技术装备production equipment 出产设备life cycle cost (LCC) 寿命周期费用mangement regulation of lubricant warehouse 润滑油库办理制度commodity inspection 商检〔商品查验〕combination of design, manufacturing and operation 设计、制造与使用相结合investigation on plant 设备调研reliability reliability theory 设备的可靠性与可靠度energy saving property of plant 设备的节能性facility inspection and appraise through comparison for plant 设备的查抄评比plant check system 设备点检制度environmental protection property of plant 设备的环保性complete set of plant 设备的成套性safety of plant 设备的安然性productivity of plant 设备的出产率durability of plant 设备的耐用性flexibility of plant 设备的灵活性equipment condition monitoring and diagnostic technology manage 设备状态监测与诊断技术办理equipment condition management systen 设备状态办理制度total plant management 设备综合办理dynamic management system of plant assets 设备资产动态办理制度plant leasing 设备租赁preparation system before equipment repair 设备修前筹办制度man-hours quota for equipment repair 设备补缀工时定额expense quota for equipment repair 设备补缀费用定额material quota for equipment repair 设备补缀材料定额acceptance regulation of equipment repair quality 设备补缀质量验收制度equipment model 设备型号type of equipment 设备型式economical life of equipment 设备经济寿命operation and business management system 设备经营办理制度technical document of plant 设备技术档案technical conditions of equipment 设备技术状况technical condition management of plant 设备技术状态办理management system for technical document and file of plant 设备技术资料办理制度technical properties of plant 设备技术性能technical life of equipment 设备技术寿命specialized cooperation of plant maintenance 设备检修专业化协作planning and management regulation of plant maintenance 设备检修方案办理制度plant maintenance plan 设备检修方案plant maintenance specification 设备检修规程plant maintenance quality 设备检修质量design and construction of equipment foundation 设备根底设计与施工management of equipment order contract 设备合同办理feasibility studies of plant project 设备规划可行性阐发investment plan of plant 设备规划performance of plant 设备功能〔效能〕operational capability of plant 设备工作能力examination and check systems of plant management 设备办理查核制度economic responsibility regulation of plant management 设备办理经济责任制度post standard of plant management 设备办理岗位尺度plant management systems 设备办理制度downtime quota for equipment repair 设备办理停歇时间定额〔停歇天数〕plant engineering modernization 设备办理现代化plant management, plant enginerring 设备办理fixed plant assets management systems 设备固定资产办理制度equipment failure 设备故障plant renewal management 设备更新办理制度plant renewal 设备更新plant replacement 设备更换post responsibility of plant management 设备岗位责任equipment modification management system 设备改造办理制度plant reconstruction, plant modernization 设备改造classified management of plant 设备分级办理operation regulation with fixed qualified operator and fixed eq 设备定人定机、凭证操作规定“five disciplines〞of plant operation 设备操作的“五项纪律〞operation specification of equipment 设备操作规程management regulation of equipment spare parts 设备备品配件办理制度management regulation of equipment spare parts inventory 设备备件库房办理制度to quote plant price 设备报价discard of plant 设备报废equipment installation management 设备安装办理equipment installation 设备安装tours system to inspect plant 设备巡回查抄制度to enquire plant price 设备询价plant model selection 设备选型acceptance check and reception systems of plant 设备验收交接制度statistic-reporting system of plant 设备统计报表制度technical document and date for plant maintenance 设备维修技术资料management regulation of plant maintenance technology 设备维修技术办理制度equipment maintenance quota 设备维修定额equipment service specification 设备维护规程unit account of plant 设备台帐equipment perfectness norm 设备完好尺度plant in good condition 设备完好claims for equipment 设备索赔specifications of usage 设备使用规程information feedback management in initial operation period of pl 设备使用初期信息反响办理management regulation for operation and service of equipment 设备使用与维护办理制度life-cycle management of plant 设备全过程办理life of equipment 设备寿命lubrication management regulation of plant 设备润滑办理制度“five fixation〞of lubrication 设备润滑“五定〞accident management regulation of plant 设备变乱办理制度three do not let pass of plant accident 设备变乱“三不放过〞plant accident 设备变乱region responsibility system of plant maintenance 设备区域维修负责制fore period and later period management of plant 设备前期办理和后期办理regulation of fore period management of plant 设备前期办理规定wear compensation for plant 设备磨损抵偿plant ageing 设备老化arithmetic mean 算术平均值〔均值〕coercionary service system 强制调养制effect coefficient of investment 投资效果系数economic management system of plant 设备经济办理制度excellence selection activity in plant management 设备办理评优活动Pareto chart 摆列图〔帕累托图〕load test 负荷试验breakdown time 故障停机时间technological adaptability 工艺适应性supervision of engineering facilities 工程设备监理management of proccess-control-point equipment 工序控制点设备办理contract change and cancellation 合同变动与解除combined maintenance 混合维修regression analysis 回归阐发interval between inspections 查抄间隔期socialization of maintenance 检修社会化centralized maintenance 集中维修technical advancement 技术先进性combination of technical management and economic management 技术办理与经济办理相结合computer-aided plant management 计算机辅助设备办理P〕planned preventive maintenance system 方案预修制度〔ЛЛFOB of imported equipment 进口设备离岸价imported equipment management 进口设备办理CIF of imported equipment 进口设备到岸价precise,large scale,rare plant 精、大、稀设备management of precise,large scale,rare equipment 精、大、稀设备办理“five fixed〞of precise,large scale,rare,critical equipme 精、大、稀、关键设备的“五定〞economy 经济性static test 静态试验open-case inspection 开箱查抄average deviation 平均偏差mean waiting time,MWT 平均等待时间repair cycle 补缀周期structure of repair cycle 补缀周期布局combination of repair, modernization and renewal 补缀、改造与更新相结合complexity coefficient of repair 补缀复杂系数time between repairs 补缀间隔期leased equipment management system 租赁设备办理制度time value of fund 资金的时间价值natural accident 自然变乱self-made equipment 便宜设备management system for selfmade equipment 便宜设备办理制度self-made spare parts management system 便宜备件办理制度combination of professional management and mass management 专业办理与群众办理相结合transfer of facility 转让设备〔设备调剂〕typical investigation 典型查询拜访areal (departmental) repair center 地域〔部分〕补缀中心recovery ratio of used oil 废油回收率perfectness ratio of power plant 动力设备完好率fulfillment ratio of periodic service 按期调养完成率mean downtime(days) due to overhaul 大补缀平均停歇天数perfectness ratio of key-point equipments 重点设备完好率qualification ratio under first acceptance check 一次交验合格率availability of plant in use 在用设备可操纵率utilization ratio of installed equipments 已安装设备操纵率annual profit ratio per 10000 yuan fixed assets 万元固定资产年创利润率maintenance expense for 1000 yuan production value 万元产值占用维修费用installation ratio of owned equipments 实有设备安装率comprehensive utilization ratio of plant 设备综合操纵率added value rate of plant assets 设备资产增值率capital investment recovery period of plant 设备资产投资回收期newness degree of plant 设备新度profit ratio vs net book value of plant 设备净资产创利润率utilization ratio of planned time of plant 设备方案台时操纵率constitution ratio of plant 设备构成比load rate of plant 设备负荷率back repair rate 设备返修率utilization ratio of institutional time of plant 设备制度台时操纵率idelness ratio of plant 设备闲置率plant capital investment recovery ratio 设备投资回收报率capital investment recovery period of plant 设备投资产出比perfectness ratio of plant 设备完好率plant daily service fulfillment ratio 设备日常调养完成率incident frequency 设备变乱频率utilization ratio 设备操纵率down time ratio to accident (failure) 变乱［故障］停机率fulfillment ratio of cleaning and oil change plan 清洗换油方案完成率mean repair cost per complexity coefficient of repair 每个补缀复杂系数平均大补缀成本maintenance expense per repair complexity coefficient 每个复杂系数占用维修费用industrial increase value ratio per 10000 yuan fixed assets 每万元固定资产创工业增加值率failure intensity 故障强度failure frequency 故障频率perfectness ratio of critical equipments 关键设备完好率perfectness raito of precise,large scale and rare equipments 精大稀设备完好率availability 可操纵率〔有效操纵率〕mean down time,MDT 平均停机时间mean time between failture 平均故障间隔期，平均无故障工作时间fulfillment ratio of repair plan 补缀方案完成率。
基于熵最小化的LFM信号调频率估计算法
收稿日期：2016-03-25修回日期：2016-04-10基金项目：军队预研基金资助项目（51333030103）作者简介：袁园（1990-），女，河南洛阳人，助理工程师。
研究方向：通信对抗。
*摘要：利用LFM 信号频谱的熵随着调频率减小而降低的性质，提出了一种基于频谱熵最小化的LFM 信号调频率的估计SEM 方法。
建立参数待估的相位补偿因子，通过搜索得到使得补偿后信号频谱熵全局最小的调频率估值。
在搜索过程中，采用两级搜索策略，并引入牛顿迭代算法，有效降低了算法复杂度。
理论推导和仿真结果证明，该算法为有偏算法，估计偏差量与初始频率相关，理论估计方差比较CR 下界低12dB 。
对雷达实测回波信号进行验证，与离散多项式变换算法相比发现，提出算法估计的鲁棒性更好，并具有较高的测速精度，具有一定的应用价值。
关键词：LFM 信号，最小熵，有偏估计，Cramer-Rao 下界中图分类号：TN911.7文献标识码：A基于熵最小化的LFM 信号调频率估计算法*袁园，蔡啸，郭蓓蓓（中国洛阳电子装备试验中心，河南洛阳471003）Estimation Method of LFM Signal Chirp RateBased on Entropy MinimizationYUAN Yuan ，CAI Xiao ，GUO Bei-bei（Luoyang Electronic Equipment Testing Center ，Luoyang 471003，China ）Abstract ：Based on the fact that the spectrum entropy decreases with the chirp rate being smaller ，this paper proposes a spectrum entropy minimization （SEM ）based chirp rate estimation method.A phase filter is established and the chirp rate estimation is accomplished via minimization of the spectrum entropy.In this process ，a two-step search strategy is utilized.In step one ，a large searching step is chosen to achieve the coarse estimation of the parameter and then Newton iterative search algorithm is used in step two to estimation the chirp rate accurately.Theoretical derivation shows that the proposed algorithm is biased ，which is related to the fractional part of the initial frequency and the variance is about 12dB lower than Cramer-Rao lower bound.Simulation result proves the correctness of the derivation and the comparison with classic discrete polynomial phase transform is made.Key words ：LFM signal ，minimum entropy ，biased estimation ，cramer-rao lower bound 0引言线性调频（Linear Frequency Modulation ，LFM ）信号以其良好的时域压缩特性和大的发射能量等诸多优点，在雷达、声呐、生物医学及通信工程等领域得到了广泛应用。
数学专业词汇
数学专业词汇Aabsolute value 绝对值 accept 接受 acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析 analysis of covariance 协方差分析 analysis of variance 方差分析 arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验 availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布 between groups 组间的 bias 偏倚 binomial distribution 二项分布 binomial test 二项检验Ccalculate 计算 case 个案 category 类别 center of gravity 重心 central tendency 中心趋势 chi-square distribution 卡方分布 chi-square test 卡方检验 classify 分类 cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对照components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性 constant 常数continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差 covariance matrix 协方差矩阵 critical point 临界点critical value 临界值 crosstab 列联表cubic 三次的，立方的 cubic term 三次项 cumulative distribution function 累加分布函数 curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数 dependent variable 因变量 description 描述 design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断 dimension 维 discrete variable 离散变量discriminant function 判别函数 discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等 effects of interaction 交互效应 efficiency 有效性eigenvalue 特征值 equal size 等含量 equation 方程error 误差 estimate 估计 estimation of parameters 参数估计 estimations 估计量 evaluate 衡量 exact value 精确值expectation 期望 expected value 期望值 exponential 指数的 exponential distributon 指数分布 extreme value 极值F factor 因素，因子 factor analysis 因子分析 factor score 因子得分factorial designs 析因设计factorial experiment 析因试验 fit 拟合fitted line 拟合线 fitted value 拟合值 fixed model 固定模型 fixed variable 固定变量 fractional factorial design 部分析因设计 frequency 频数F-test F检验full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值 heterogeneity 不齐性histogram 直方图 homogeneity 齐性 homogeneity of variance 方差齐性hypothesis 假设 hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估计intraclass correlation 组间相关 inverse 倒数的iterate 迭代Kkernal 核 Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验 kurtosis 峰度Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数 least-square estimation 最小二乘估计 least-square method 最小二乘法level 水平level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数 likelihood ratio test 似然比检验 linear 线性的 linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系 linear term 线性项 logarithmic 对数的logarithms 对数 logistic 逻辑的 lost function 损失函数Mmain effect 主效应 matrix 矩阵 maximum 最大值 maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差 mean sum of square 均方和 measure 衡量media 中位数M-estimator M估计minimum 最小值missing values 缺失值 mixed model 混合模型 mode 众数model 模型Monte Carle method 蒙特卡罗法 moving average 移动平均值multicollinearity 多元共线性multiplecomparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数 multiple regression analysis 多元回归分析 multiple regression equation 多元回归方程 multiple response 多响应 multivariate analysis 多元分析Nnegative relationship 负相关nonadditively 不可加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验 normal distribution 正态分布 null hypothesis 零假设 number of cases 个案数Oone-sample 单样本 one-tailed test 单侧检验 one-way ANOVA 单向方差分析 one-way classification 单向分类 optimal 优化的optimum allocation 最优配制order 排序order statistics 次序统计量origin 原点orthogonal 正交的outliers 异常值Ppaired observations 成对观测数据 paired-sample 成对样本 parameter 参数parameter estimation 参数估计 partial correlation 偏相关partial correlation coefficient 偏相关系数 partial regression coefficient 偏回归系数 percent百分数percentiles 百分位数pie chart 饼图point estimate 点估计poisson distribution 泊松分布polynomial curve 多项式曲线 polynomial regression 多项式回归polynomials 多项式positive relationship 正相关power 幂P-P plot P-P概率图 predict 预测 predicted value 预测值 prediction intervals 预测区间 principal component analysis 主成分分析 proability 概率 probability density function 概率密度函数probit analysis 概率分析proportion 比例Qqadratic 二次的 Q-Q plot Q-Q概率图 quadratic term 二次项 quality control 质量控制 quantitative 数量的，度量的quartiles 四分位数Rrandom 随机的 random number 随机数 random number 随机数random sampling 随机取样 random seed 随机数种子 random variable 随机变量 randomization 随机化 range 极差 rank 秩rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析 regression coefficient 回归系数 regression line 回归线 reject 拒绝 rejection region 拒绝域 relationship 关系 reliability 可*性 repeated 重复的 report 报告，报表 residual 残差 residual sum ofsquares 剩余平方和 response 响应 risk function 风险函数robustness 稳健性 root mean square 标准差 row 行 run 游程 run test 游程检验Sample 样本 sample size 样本容量 sample space 样本空间sampling 取样 sampling inspection 抽样检验 scatter chart 散点图 S-curve S形曲线 separately 单独地 sets 集合 sign test 符号检验 significance 显著性 significance level 显著性水平 significance testing 显著性检验 significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布 skewness 偏度 small sample problem 小样本问题 smooth 平滑 sort 排序 soruces of variation 方差来源space 空间spread 扩展square 平方standard deviation 标准离差 standard error of mean 均值的标准误差standardization 标准化 standardize 标准化 statistic 统计量statistical quality control 统计质量控制std. residual 标准残差 stepwise regression analysis 逐步回归stimulus 刺激strong assumption 强假设stud. deleted residual 学生化剔除残差stud. residual 学生化残差subsamples 次级样本 sufficient statistic 充分统计量 sum 和 sum of squares 平方和 summary 概括，综述Ttable 表 t-distribution t分布 test 检验 test criterion 检验判据 test for linearity 线性检验 test of goodness of fit 拟合优度检验 test of homogeneity 齐性检验 test of independence 独立性检验test rules 检验法则test statistics 检验统计量testing function 检验函数time series 时间序列 tolerance limits 容许限 total 总共，和transformation 转换 treatment 处理 trimmed mean 截尾均值 true value 真值 t-test t检验 two-tailed test 双侧检验Uunbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性 uniform distribution 均匀分布Vvalue of estimator 估计值 variable 变量 variance 方差variance components 方差分量variance ratio 方差比various 不同的 vector 向量Wweight 加权，权重 weighted average 加权平均值 within groups 组内的ZZ score Z分数2. 最优化方法词汇英汉对照表Aactive constraint 活动约束 active set method 活动集法analytic gradient 解析梯度 approximate 近似 arbitrary 强制性的 argument 变量 attainment factor 达到因子Bbandwidth 带宽 be equivalent to 等价于 best-fit 最佳拟合 bound 边界Ccoefficient 系数complex-value 复数值component 分量constant 常数constrained 有约束的constraint 约束constraint function 约束函数 continuous 连续的 converge 收敛 cubic polynomial interpolation method三次多项式插值法 curve-fitting 曲线拟合Ddata-fitting 数据拟合 default 默认的，默认的 define 定义diagonal 对角的direct search method 直接搜索法direction of search 搜索方向 discontinuous 不连续Eeigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的Ffeasible 可行的feasible solution 可行解finite-difference 有限差分 first-order 一阶GGauss-Newton method 高斯-牛顿法 goal attainment problem 目标达到问题 gradient 梯度 gradient method 梯度法Hhandle 句柄 Hessian matrix 海色矩阵Independent variables 独立变量inequality 不等式infeasibility 不可行性infeasible 不可行的initial feasible solution 初始可行解 initialize 初始化 inverse 逆 invoke 激活 iteration 迭代 iteration 迭代JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子large-scale 大型的least square 最小二乘 least squares sense 最小二乘意义上的 Levenberg-Marquardt method 列文伯格-马夸尔特法 line search 一维搜索linear 线性的linear equality constraints 线性等式约束 linear programming problem 线性规划问题 local solution 局部解M medium-scale 中型的 minimize 最小化 mixed quadraticand cubic polynomial interpolation and extrapolation method 混合二次、三次多项式内插、外插法 multiobjective 多目标的Nnonlinear 非线性的 norm 范数Oobjective function 目标函数observed data 测量数据optimization routine 优化过程 optimize 优化 optimizer 求解器 over-determined system 超定系统Pparameter 参数partial derivatives 偏导数polynomial interpolation method 多项式插值法Qquadratic 二次的 quadratic interpolation method 二次内插法 quadratic programming 二次规划Rreal-value 实数值residuals 残差robust 稳健的robustness 稳健性，鲁棒性S scalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method 序列二次规划法simplex search method 单纯形法 solution 解 sparse matrix 稀疏矩阵 sparsity pattern 稀疏模式 sparsity structure 稀疏结构 starting point 初始点 step length 步长 subspace trust region method 子空间置信域法 sum-of-squares 平方和symmetric matrix 对称矩阵Ttermination message 终止信息 termination tolerance 终止容限 the exit condition 退出条件 the method of steepest descent 最速下降法 transpose 转置Uunconstrained 无约束的 under-determined system 负定系统Vvariable 变量 vector 矢量Wweighting matrix 加权矩阵3 样条词汇英汉对照表Aapproximation 逼近array 数组 a spline in b-form/b-spline b样条 a spline of polynomial piece /ppform spline 分段多项式样条Bbivariate spline function 二元样条函数 break/breaks 断点Ccoefficient/coefficients 系数 cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式cubic smoothing spline 三次平滑样条cubic spline 三次样条cubic spline interpolation 三次样条插值/三次样条内插curve 曲线Ddegree of freedom 自由度 dimension 维数Eend conditions 约束条件input argument 输入参数interpolation 插值/内插 interval 取值区间Kknot/knots 节点Lleast-squares approximation 最小二乘拟合Mmultiplicity 重次 multivariate function 多元函数Ooptional argument 可选参数 order 阶次 output argument 输出参数P point/points 数据点Rrational spline 有理样条 rounding error 舍入误差（相对误差）Sscalar 标量 sequence 数列（数组） spline 样条 spline approximation 样条逼近/样条拟合spline function 样条函数spline curve 样条曲线 spline interpolation 样条插值/样条内插 spline surface 样条曲面 smoothing spline 平滑样条Ttolerance 允许精度Uunivariate function 一元函数Vvector 向量Wweight/weights 权重4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图 converge 收敛 coordinate 坐标系Ddecomposed 分解的 decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditions Dirichlet边界条件Eeigenvalue 特征值 elliptic 椭圆形的 error estimate 误差估计 exact solution 精确解Ggeneralized Neumann boundary condition 推广的Neumann边界条件 geometry 几何形状 geometry description matrix 几何描述矩阵geometry matrix 几何矩阵graphical user interface（GUI）图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子 Laplace equation 拉普拉斯方程 linear interpolation 线性插值 loop 循环Mmachine precision 机器精度 mixed boundary condition 混合边界条件NNeuman boundary condition Neuman边界条件 node point 节点 nonlinear solver 非线性求解器 normal vector 法向量PParabolic 抛物线型的 partial differential equation 偏微分方程plane strain 平面应变plane stress 平面应力Poisson's equation 泊松方程polygon 多边形positive definite 正定Qquality 质量Rrefined triangular mesh 加密的三角形网格relative tolerance 相对容限 relative tolerance 相对容限 residual 残差 residual norm 残差范数Ssingular 奇异的。
精选数理化学科常考英文词汇
精选数理化学科常考英文词汇work Information Technology Company.2020YEAR数理化学科常考英文词汇汇总数学（107个）：词汇释义assume that 假设approximation 近似，近似值absolute value 绝对值acute 锐（角）adjacent angle 邻角alternate angles 内错角angle 角area 面积arithmetic sequence 等差数列assumption 假设asymptote 渐近线at random 随机地average 平均的axis 轴base 底面，底数be inscribed in 内接于binomial 二项式circle 圆circumference 周长clockwise 顺时针的common difference (等差数列的)公差common divisor 公约数common ratio (等比数列的)公比common multiple 公倍数composite number 合数cone 圆锥congruent 全等的constant 不变的；常数coordinate 坐标cube 立方体cube root 立方根cylinder 圆柱体decimal 小数diagonal 对角线digit 数字，位divide 除divisible 可整除的domain 定义域eccentricity 离心率elipse 椭圆equilateral 等边的even 偶的exponent 指数fraction 分数function 函数geometric sequence 等比数列hyperbola 双曲线inequality 不等式infinite 无穷的integer 整数intercept 截距interior angle 内角intersect 相交irrational number 无理数isosceles 等腰的major axis 长轴mean 平均数median 中数minor axis 短轴minus 减mode 众数multiply 乘negative 负的number line 数轴obtuse 钝（角）odd 奇的origin of coordinates 原点parallel 平行的parallelogram 平行四边形perimeter 周长perpendicular 垂直的plus 加polynomial 多项式positive 正的prime number 质数probability 概率product 积proportion 比例quadruple 四倍的quotient 商radian 弧度radius 半径range 值域rational number 有理数reciprocal 倒数rectangle 矩形right 直(角）scalene 不等边的，不等边三角形section 截面sector 扇形segment 线段similar 相似的slope 斜率sphere 球体square 正方形square root 平方根standard deviation 标准差sum 和tangent 相切term 项translate 移动trapezoid 梯形triangle 三角形triple 三倍value 值vector 矢量vertex 顶点物理（127个）词汇释义acceleration 加速度anion 阴离子ammeter 安培表amplitude 振幅band 条,带bar 条,带bombard 轰击cation 阳离子capacitor 电容centripetal force 向心力circuit 电路coherent 相干的coil 线圈collision 碰撞comet 彗星convection 对流converging lens 凸透镜coulomb 库仑critical angle 临界角decay 衰变deflecte 偏转density 密度diffraction 衍射dilation 伸长diminish 减小discrete 离散的，不连续的diverge 分开，分岔diverging lens 凹透镜elastic 弹性的electric generator 发电机electric motor 电动机electromotive force(e.m.f.) 电动势elctron capture 电子捕获emission 散发，发射entropy 熵estimate 估计excited state 激发态exert 施加expansion 膨胀fiber optic 光导纤维focal length 焦距spring(or force) constant (弹簧的)倔强系数frequency 频率frictionless 光滑无摩擦的gravity 重力ground state 基态half-life 半衰期halve 减半的horizontal 水平的hydraulic jack 液压千斤顶impinge 撞击incident ray 入射光index of refraction 折射率induction current 感应电流inertia 惯性initial 初始的interference 干涉internal 内部的isotope 同位素kinetic energy 动能latent heat 潜热lever 杠杆longitudinal wave 纵波magnetic 磁的magnetic flux 磁通量magnify 扩大magnitude 大小mass 质量matter wave 物质波moment 力矩momentum 动量negligible 可忽略的neutron 中子nuclear fission 核裂变nuclear fusion 核聚变optic 光学的oscillate 振动，摇摆parabola 抛物线parallel 并联particle 粒子pendulum 钟摆permanent 永久的photon 光子pitch 音高polarization 偏振positron 正电子potential energy 势能power 功率propagation 传播proton 质子pulley 滑轮radioactive 放射性refracte 折射relativity 相对性resistor 电阻rest 静止revolution 一周rigid 刚性的scalar 标量semiconductor 半导体series 串联sign （电量等的）符号simple harmonic motion 简谐运动simultaneously 同时地slit 狭缝solenoid 螺线管spectrum 光谱，波谱speed 速率sphere 球体spring 弹簧standing wave 驻波superconductor 超导体superimpose 叠加tesla 特斯拉(磁强单位)thermal 热量的thermodynamics 热力学torque 转矩，扭矩total reflection 全反射transition 跃迁transverse wave 横波uniform 均匀的velocity 速度virtual image 虚像voltage 电压voltmeter 电压表wavelength 波长wave-particle duality 波粒二象性化学（156个）：词汇释义acid 酸activated complex 活化络合物activation energy 活化能aggregate 聚合alkali metals 碱金属alkaline earth metals 碱土金属alkane 烷烃alkene 烯烃alkyne 炔烃allotropy 同素异形体alloy 合金aluminum 铝ammonia 氨amorphous 非晶体amphoteric 两性的anode 阳极anomalous 不规则的aqueous 水溶液argon 氩Avogadro's law 阿佛加德罗定律barium 钡bauxite 铝土矿bleaching 漂白bond 键boron 硼brass 黄铜bromine 湨buret 滴定管calcium 钙calory 卡路里carbohydrate 碳水化合物carbon dioxide 二氧化碳carbon monoxide 一氧化碳carbonate 碳酸盐carboxylic acid 羧酸catalyst 催化剂cathode reaction 阴极反应cellulose 纤维素chlorine 氯chromium 铬coefficient 系数combination reaction 化合反应combustion 燃烧composition 组成compound 化合物concentrated 浓的concentration 浓度condensation 冷凝covalent bond 共价键cracking 裂解crude oil 原油crystal 晶体deoxyribose 脱氧核糖diatomic molecule 双原子分子diffusion 扩散dilute 稀的displacement reaction 置换反应distillation 蒸馏double bonds 双键dynamic equilibrium 动态平衡electrolysis 电解elcetrolyte 电解质electronic configuration 电子排布element 元素empirical formula 经验式endothermic 吸热的enthalpy 焓erosion 腐蚀ethanoic acid 乙酸ethanol 乙醇ethene 乙烯evaporation 蒸发exothermic 放热的extraction 提炼filtering 过滤flame test 焰色反应fluorine 氟fractional distillation 分馏freezing point 凝固点glucose 葡萄糖glycogen 糖原graphite 石墨greenhouse effect 温室效应Haber process 哈伯法(制氨)halogen 卤素helium 氦homologous series 同系物hydrocarbon 烃hydrogen 氢hydrogen chloride 氯化氢hydrogen peroxide 过氧化氢hydronium ion 水合氢离子hydroxide 氢氧根indicator 指示剂iodine 碘isomerism 同素异形体le Chatelier's principle 勒沙特列原理lead 铅limestone 石灰石linear 直线的lipid 脂质，类脂lithium 锂litmus 石蕊magnesium 镁metalloid 类金属methane 甲烷methanoic acid 甲酸methanol 甲醇monomer 单体neon 氖neutralization 中和nickel 镍nitrate 硝酸盐nitric acid 硝酸nitrogen 氮noble gases 稀有气体oxide 氧化物oxidation agent 氧化剂ozone 臭氧periodic table 元素周期表permanganate 高锰酸petroleum 石油phenolphthalein 酚酞phosphorus 磷planar 平面的platinum 铂polar 极性的polymer 聚合物potassium 钾precipitation 沉淀propane 丙烷propanoic acid 丙酸propanol 丙醇propene 丙烯pure substance 纯净物reactive 活泼的redox 氧化还原reducing agent 还原剂reversible reaction 可逆反应shared paris of electrons 共用电子对silicon 硅sodium钠solvent 溶剂starch 淀粉sublime 升华sulphate 硫酸盐sulphur 硫sulphuric acid 硫酸suspension 悬浮液tetrahedral 四面体titration 滴定torr 托耳(压强单位)triple bonds 三键van der Waals' force 范德华力volatile 易挥发的zinc 锌11。
基于FPGA离散分数阶傅里叶变换算法的实现
基于FPGA离散分数阶傅里叶变换算法的实现史兆强;魏增辉;马壮【摘要】In order to implement the DFRFT （discrete fractional 傅里叶transform） algorithm on FPGA （field programmable gate array）, some DFRFT methods are analyzed and the Ozaktas＇s DFRFT fast algorithm is selected to achieve the implementation on FPGA. On the basis of theoretical analysis for the algorithm, the computing process of fast algorithm is optimized, and the simulation results is given. Put forward a detailed program to achieve on FPGA under ensuring the accuracy of the request. The practical application of engineering shows that the solution has excellent performance.%为在可编程逻辑门阵列（FPGA）上实现离散分数阶傅里叶变换（DFRFT），对多种DFRFT算法进行比较分析，并选用Ozaktas提出的离散快速算法做了基于FPGA的实现。
在对该算法进行理论分析的基础上，对快速算法的计算过程做优化处理，并给出仿真结果比较。
在保证精度要求下，提出详细的FPGA实现方案。
工程实际应用表明：该方法具有优良性能。
【期刊名称】《河南机电高等专科学校学报》【年(卷),期】2012(020)002【总页数】3页(P17-19)【关键词】离散分数阶傅里叶变换;现场可编程逻辑阵列;FFT核【作者】史兆强;魏增辉;马壮【作者单位】河南机电高等专科学校电子通信工程系,河南新乡453000;黄河水利职业技术学院信息工程系,河南开封475003;中国电子科技集团公司第二十七研究所,河南郑州450047【正文语种】中文【中图分类】TN911.721 引言分数阶傅里叶变换是对经典傅里叶变换的推广，在分析和处理非平稳信号领域有着广泛的应用。
科学文献
Abstract In standard fractal terrain models based on fractional Brownian motion the statistical character of the surface is, by design, the same everywhere. A new approach to the synthesis of fractal terrain height fields is presented which, in contrast to previous techniques, features locally independent control of the frequencies composing the surface, and thus local control o f fractal dimension and other statistical characteristics. The new technique, termed noise synthesis, is intermediate in difficulty of implementation, between simple stochastic subdivision and Fourier filtering or generalized stochastic subdivision, and doe s not suffer the drawbacks of creases or periodicity. Varying the local crossover scale of fractal character or the fractal dimension with altitude or other functions yi
试题英文数理统计
一、填空（一）各章节的introduction1、Continuous variables or interval data can assume any value in some interval of real numbers.连续变量或间隔数据可以假设在某个实数间隔中的任意值。
（measurement）Discrete variables assume only isolated values.离散变量只假定孤立的值。
(counting)11、The lower or first quartile is the 25th percentile and the upper or third quartile is the 75th percentile.12、The fist qurtile Q1 is the median of the observations falling below the median of the entire sample and the third quartile Q3 is the median of the observations falling above the median of the entire sample.The interquartile range is defined as IQR=Q3-Q1.第一个四分位数Q1是低于整个样本中位数的观测值的中位数，第三个四分位数Q3是高于整个样本中位数的观测值的中位数。
四分位数范围定义为IQR=Q3-Q1。
2、Statistics applied to the life sciences in often called biostatistics or biometry.统计学应用于生命科学，通常称为生物统计学或生物计量学。
3、A descriptive measure associated with a random variable when it is considered over the entire population is called a parameter.当在整个总体中考虑一个随机变量时，与它相关的描述性度量称为参数4、One is forced to examine a subset or sample of the population and make inferences about the entire variable of a sample is called a statistic.人们被迫检查总体中的一个子集或样本，并对样本中的整个变量做出推断，这被称为统计量。
计算机专业英语单词
Abbreviations
LIFO (last-in, first-out) 后进先出
FIFO (first-in, first-out) 先进先出
4.3 Queues
New Words &n.行列, 队列; vi.排队
cafeteria n.自助餐厅
rear n.后面, 背后, 后方
documentation n.文件
debugging n.调试
spreadsheet n.电子制表软件, 电子数据表
Abbreviations
CASE (computer-aided software engineering) 计算机辅助软件工程
GUI (Graphical User Interfaces) 图形用户界面
microkernel n.微核
portability n.可移植性
extensibility n.可延长性, 展开性
stratify vt. 分层，层化
hierarchy n.层次,层级
detract v.转移
devise vt.设计, 发明, 图谋, 作出
not-so-small 并不十分小
real time 实时
2.1 Basic Organization of Computers
New Words & Expressions: instruction cycle 指令周期 bus n. 总线 uppermost adj.最高的；adv.在最上 data bus 数据总线 multibit 多位 unidirectional 单向的 microprocessor n.微处理器 timing n.定时；时序；时间选择 assert vt.主张，发出 trigger vt.引发, 引起, 触发 port n.端口
纹理物体缺陷的视觉检测算法研究--优秀毕业论文
摘 要
在竞争激烈的工业自动化生产过程中，机器视觉对产品质量的把关起着举足 轻重的作用，机器视觉在缺陷检测技术方面的应用也逐渐普遍起来。与常规的检 测技术相比，自动化的视觉检测系统更加经济、快捷、高效与 安全。纹理物体在 工业生产中广泛存在，像用于半导体装配和封装底板和发光二极管，现代 化电子 系统中的印制电路板，以及纺织行业中的布匹和织物等都可认为是含有纹理特征 的物体。本论文主要致力于纹理物体的缺陷检测技术研究，为纹理物体的自动化 检测提供高效而可靠的检测算法。 纹理是描述图像内容的重要特征，纹理分析也已经被成功的应用与纹理分割 和纹理分类当中。本研究提出了一种基于纹理分析技术和参考比较方式的缺陷检 测算法。这种算法能容忍物体变形引起的图像配准误差，对纹理的影响也具有鲁 棒性。本算法旨在为检测出的缺陷区域提供丰富而重要的物理意义，如缺陷区域 的大小、形状、亮度对比度及空间分布等。同时，在参考图像可行的情况下，本 算法可用于同质纹理物体和非同质纹理物体的检测，对非纹理物体 的检测也可取 得不错的效果。 在整个检测过程中，我们采用了可调控金字塔的纹理分析和重构技术。与传 统的小波纹理分析技术不同，我们在小波域中加入处理物体变形和纹理影响的容 忍度控制算法，来实现容忍物体变形和对纹理影响鲁棒的目的。最后可调控金字 塔的重构保证了缺陷区域物理意义恢复的准确性。实验阶段，我们检测了一系列 具有实际应用价值的图像。实验结果表明 本文提出的纹理物体缺陷检测算法具有 高效性和易于实现性。 关键字: 缺陷检测；纹理；物体变形；可调控金字塔；重构
Keywords: defect detection, texture, object distortion, steerable pyramid, reconstruction
II
数学中英文词汇对照表
集合 set非负整数集the set of all non-negative integers 自然数集 the set of all natural numbers整数集 the set of all positive integers有理数集 the set of all rational numbers实数集 the set of all real numbers元素 element属于 belong to不属于 not belong to有限集 finite set无限集 infinite set空集 empty set包含 inclusion ,include包含于 lie in子集 subset真子集 proper subset补集（余集）complementary set全集 universe交集 intersection偶数集 the set of all even numbers奇数集 the set of all odd numbers含绝对值的不等式 inequality with absolute value 一元二次不等式 one-variable quadratic inequality 逻辑 logic逻辑联结词 logical connective或 or且 and非 not真 true假 false真值表 truth table原命题 original proposition逆命题 converse proposition否命题 negative proposition逆否命题 converse-negative proposition充分条件 sufficient condition必要条件 necessary condition……的充要条件是………if and only if…函数 function自变量 argument定义域domain值域 range区间 interval闭区间 closed interval开区间open interval函数的图像 graph of function映射mapping象 image原象 inverse image单调monotone增函数 increasing function减函数 decreasing function单调区间 monotone interval反函数 inverse function指数 exponentN次方根 nth root根式 radical根指数 radical exponent被开方数 radicand指数函数 exponential function对数logarithm常用对数common logarithm自然对数natural logarithm对数函数 logarithmic function数列 sequence of number项 term通项公式 the formula of general term有穷数列 finite sequence of number无穷数列 infinite sequence of number递推公式 recurrence formula等差数列 arithmetic progression公差arithmetic series等差中项common difference等比中项 arithmetic mean等比数列 geometric progression, geometric series 公比 common ratio等比中项 geometric mean三角函数 trigonometric function始边 initial side终边 terminal side正角 positive angle负角 negative angle零角zero angel象限角 quadrant angle弧度radian弧度制 radian measure角度制 degree measure正弦sine余弦cosine正切 tangent余切 cotangent正割 secant余割 cosecant诱导公式 induction formula正弦曲线sine curve余弦曲线cosine curve最大值maximum最小值minimum周期 period最小正周期minimal positive period周期函数 periodic function振幅 amplitude of vibration频率frequency相位 phase初相 initial phase反正弦 arc sine反余弦 arc cosine反正切arc tangent有向线段directed line segment向量 vector零向量 zero vector单位向量 unit vector平行向量 parallel vectors相等向量 equal vectors共线向量 collinear vectors实数与向量的积 multiplication of vector by scalar 基底 base数量积 translation正弦定理 inner product余弦定理 sine theorem算术平均数 arithmetic mean几何平均数 method of compare比较法 method of compare综合法 method of synthesis分析法 method of analysis倾斜角 gradient斜率 point slope form点斜式 gradient intercept form截距 general form斜截式 included angle两点式 two-point form一般式 general form夹角included angle线性规划 linear programming约束条件 constraint condition目标函数 objective function可行域 feasible region最优解 optimal solution曲线 curve坐标法 method of coordinate解析几何 analytic geometry笛卡儿 Descartes标准方程 standard equation一般方程 general equation参数方程 parameter equation参数 parameter圆锥曲线 point conic椭圆 ellipse焦点 focus, focal points焦距 focal length长轴 major axis短轴 minor axis离心率 eccentricity双曲线 hyperbola实轴 real axis虚轴 imaginary axis渐近线 asymptote抛物线 parabola准线 directrix直线 line平面 plane几何体 geometric solid平面图形 plane figure立体图形 slid figure相交直线 intersecting lines平行直线 parallel lines异面直线 skew lines垂线 perpendicular line垂足 foot of a oblique line垂线段 perpendicular line segment公垂线 common perpendicular line公垂线段 common perpendicular segment 垂面 perpendicular plane射影 projection斜线 oblique line斜足foot of a oblique line斜线段 oblique line segment半平面 semi-plane二面角 dihedral angle平面角 plane angle直二面角 right dihedral angle棱柱 prism底面base顶点 vertex面 face棱 edge侧面 lateral face侧棱 lateral edge斜棱柱 oblique prism直棱柱 right prism正棱柱 regular prism平行六面体 parallelepiped长方体 rectangular prism正方体 cube棱锥pyramid正棱锥 regular pyramid多面体 polyhedron凸多面体 convex polyhedron正多面体 regular polyhedron简单多面体 simple polyhedron球 solid sphere, spheroid球心 center of a solid sphere球面 sphere分类计数原理 classified enumeration principle 分步计数原理 fractional enumeration principle 排列 arrangement, permutation排列数 number of arrangements全排列 total arrangement阶乘 factorial组合 combination组合数 number of combination二项式定理 binomial theorem二项式系数 binomial coefficient二项式展开式 binomial expansion必然事件 certain event不可能事件 impossible event随机事件 random event试验 trial频率 frequency等可能事件 equiprobability event基本事件 elementary event概率 probability互斥事件 exclusive events对立事件 complementary events相互独立事件 mutually independent events 独立重复试验 independent repeated trials 概率 probability统计 statistics随机变量 random variable离散型随机变量discrete random variable概率分布 probability distribution分布列 distribution series数学期望 mathematical expectation方差 variance标准差 standard deviation抽样方法 sampling method简单随机抽样 simple random sampling系统抽样 systematic sampling总体分布 population sampling估计 estimation正态分布 normal distribution标准正态分布 standard normal distribution 线性回归 linear regression相关 correlation回归分析 regression analysis散点图 scatter diagram回归直线 regression straight line线性回归分析 liner regression analysis相关系数 correlation coefficient假设检验 hypothesis testing归纳法 induction数学归纳法 mathematical induction完全归纳法 complete induction不完全归纳法 incomplete induction极限 limit无穷大 infinitely great无穷等比数列 infinite geometric sequence 左极限 left limit右极限 right limit连续（的） continuous连续函数 continuous function导数 derivative可导的 differentiable变化率rate of change导函数derived function复合函数 composite function极大值 maximum value极小值 minimum value极值 extreme value虚数单位 imaginary unit复数 complex number复数集 set of complex numbers虚数imaginary number纯虚数 purely imaginary number复数的代数形式 algebraic form of complex number实部 real part虚部 imaginary part复平面 complex plane实轴 real axis虚轴 imaginary axis模 modulus辐角 argument复数的三角形式 trigonometric form of complex number 棣莫弗公式 De Moivre’s Formula分式 fraction通分 changing fractions to a common denominator约分 reduction of a fraction分式方程 fractional equation反比例函数 inverse proportional function双曲线 hyperbola定理 theorem平行四边形 parallelogram矩形 rectangle菱形 rhombus正方形 square梯形 trapezium等腰梯形 isosceles trapezium重心 barycenter加权平均数 weighted average权 weight中位数 median众数 mode极差 range方差 variance平面图形 plane figure展开图 net体 solid面 surface线 line点 point相交 intersection交点 point of intersection 中点 center距离 distance角 angle度 degree角的平分线 angular bisector 余角 complementary angle补角补角 supplementary angle。
傅里叶变换
傅里叶变换那么，到底什么是傅里叶变换算法列?傅里叶变换所涉及到的公式具体有多复杂列?傅里叶变换(Fourier transform)是一种线性的积分变换。
因其基本思想首先由法国学者傅里叶系统地提出，所以以其名字来命名以示纪念。
哦，傅里叶变换原来就是一种变换而已，只是这种变换是从时间转换为频率的变化。
这下，你就知道了，傅里叶就是一种变换，一种什么变换列?就是一种从时间到频率的变化或其相互转化。
ok，咱们再来总体了解下傅里叶变换，让各位对其有个总体大概的印象，也顺便看看傅里叶变换所涉及到的公式，究竟有多复杂: 以下就是傅里叶变换的4种变体(摘自，维基百科)连续傅里叶变换一般情况下，若“傅里叶变换”一词不加任何限定语，则指的是“连续傅里叶变换”。
连续傅里叶变换将平方可积的函数f(t)表示成复指数函数的积分或级数形式。
这是将频率域的函数F(ω)表示为时间域的函数f(t)的积分形式。
连续傅里叶变换的逆变换 (inverse Fourier transform)为:即将时间域的函数f(t)表示为频率域的函数F(ω)的积分。
一般可称函数f(t)为原函数，而称函数F(ω)为傅里叶变换的像函数，原函数和像函数构成一个傅里叶变换对(transform pair)。
除此之外，还有其它型式的变换对，以下两种型式亦常被使用。
在通信或是信号处理方面，常以来代换，而形成新的变换对:或者是因系数重分配而得到新的变换对:一种对连续傅里叶变换的推广称为分数傅里叶变换(Fractional FourierTransform)。
分数傅里叶变换(fractional Fourier transform,FRFT)指的就是傅里叶变换(Fourier transform,FT)的广义化。
分数傅里叶变换的物理意义即做傅里叶变换 a 次，其中 a 不一定要为整数;而做了分数傅里叶变换之后，信号或输入函数便会出现在介于时域(time domain)与频域(frequency domain)之间的分数域(fractional domain)。
可靠性专业英语
可靠性工程质量专业英语词汇集Absolute deviation, 绝对离差Absolute number, 绝对数Absolute residuals, 绝对残差Acceleration array, 加速度立体阵Acceleration in an arbitrary direction, 任意方向上的加速度Acceleration normal, 法向加速度Acceleration space dimension, 加速度空间的维数Acceleration tangential, 切向加速度Acceleration vector, 加速度向量Acceptable hypothesis, 可接受假设Accumulation, 累积Accuracy, 准确度Actual frequency, 实际频数Adaptive estimator, 自适应估计量Addition, 相加Addition theorem, 加法定理Additivity, 可加性Adjusted rate, 调整率Adjusted value, 校正值Admissible error, 容许误差Aggregation, 聚集性Alternative hypothesis, 备择假设Among groups, 组间Amounts, 总量Analysis of correlation, 相关分析Analysis of covariance, 协方差分析Analysis of regression, 回归分析Analysis of time series, 时间序列分析Analysis of variance, 方差分析Angular transformation, 角转换ANOV A （analysis of variance）, 方差分析ANOV A Models, 方差分析模型Arcing, 弧弧旋Arcsine transformation, 反正弦变换Area under the curve, 曲线面积AREG , 评估从一个时间点到下一个时间点回归相关时的误差ARIMA, 季节和非季节性单变量模型的极大似然估计Arithmetic grid paper, 算术格纸Arithmetic mean, 算术平均数Arrhenius relation, 艾恩尼斯关系Assessing fit, 拟合的评估Associative laws, 结合律Asymmetric distribution, 非对称分布Asymptotic bias, 渐近偏倚Asymptotic efficiency, 渐近效率Asymptotic variance, 渐近方差Attributable risk, 归因危险度Attribute data, 属性资料Attribution, 属性Autocorrelation, 自相关Autocorrelation of residuals, 残差的自相关Average, 平均数Average confidence interval length, 平均置信区间长度Average growth rate, 平均增长率Bar chart, 条形图Bar graph, 条形图Base period, 基期Bayes' theorem , Bayes定理Bell-shaped curve, 钟形曲线Bernoulli distribution, 伯努力分布Best-trim estimator, 最好切尾估计量Bias, 偏性Binary logistic regression, 二元逻辑斯蒂回归Binomial distribution, 二项分布Bisquare, 双平方Bivariate Correlate, 二变量相关Bivariate normal distribution, 双变量正态分布Bivariate normal population, 双变量正态总体Biweight interval, 双权区间Biweight M-estimator, 双权M估计量Block, 区组配伍组BMDP(Biomedical computer programs), BMDP统计软件包Boxplots, 箱线图箱尾图Breakdown bound, 崩溃界崩溃点Canonical correlation, 典型相关Caption, 纵标目Case-control study, 病例对照研究Categorical variable, 分类变量Catenary, 悬链线Cauchy distribution, 柯西分布Cause-and-effect relationship, 因果关系Cell, 单元Censoring, 终检Center of symmetry, 对称中心Centering and scaling, 中心化和定标Central tendency, 集中趋势Central value, 中心值CHAID -χ2 Automatic Interaction Detector, 卡方自动交互检测Chance, 机遇Chance error, 随机误差Chance variable, 随机变量Characteristic equation, 特征方程Characteristic root, 特征根Characteristic vector, 特征向量Chebshev criterion of fit, 拟合的切比雪夫准则Chernoff faces, 切尔诺夫脸谱图Chi-square test, 卡方检验χ2检验Choleskey decomposition, 乔洛斯基分解Circle chart, 圆图Class interval, 组距Class mid-value, 组中值Class upper limit, 组上限Classified variable, 分类变量Cluster analysis, 聚类分析Cluster sampling, 整群抽样Code, 代码Coded data, 编码数据Coding, 编码Coefficient of contingency, 列联系数Coefficient of determination, 决定系数Coefficient of multiple correlation, 多重相关系数Coefficient of partial correlation, 偏相关系数Coefficient of production-moment correlation, 积差相关系数Coefficient of rank correlation, 等级相关系数Coefficient of regression, 回归系数Coefficient of skewness, 偏度系数Coefficient of variation, 变异系数Cohort study, 队列研究Column, 列Column effect, 列效应Column factor, 列因素Combination pool, 合并Combinative table, 组合表Common factor, 共性因子Common regression coefficient, 公共回归系数Common value, 共同值Common variance, 公共方差Common variation, 公共变异Communality variance, 共性方差Comparability, 可比性Comparison of bathes, 批比较Comparison value, 比较值Compartment model, 分部模型Compassion, 伸缩Complement of an event, 补事件Complete association, 完全正相关Complete dissociation, 完全不相关Complete statistics, 完备统计量Completely randomized design, 完全随机化设计Composite event, 联合事件Composite events, 复合事件Concavity, 凹性Conditional expectation, 条件期望Conditional likelihood, 条件似然Conditional probability, 条件概率Conditionally linear, 依条件线性Confidence interval, 置信区间Confidence limit, 置信限Confidence lower limit, 置信下限Confidence upper limit, 置信上限Confirmatory Factor Analysis , 验证性因子分析Confirmatory research, 证实性实验研究Confounding factor, 混杂因素Conjoint, 联合分析Consistency, 相合性Consistency check, 一致性检验Consistent asymptotically normal estimate, 相合渐近正态估计Consistent estimate, 相合估计Constrained nonlinear regression, 受约束非线性回归Constraint, 约束Contaminated distribution, 污染分布Contaminated Gausssian, 污染高斯分布Contaminated normal distribution, 污染正态分布Contamination, 污染Contamination model, 污染模型Contingency table, 列联表Contour, 边界线Contribution rate, 贡献率Control, 对照Controlled experiments, 对照实验Conventional depth, 常规深度Convolution, 卷积Corrected factor, 校正因子Corrected mean, 校正均值Correction coefficient, 校正系数Correctness, 正确性Correlation coefficient, 相关系数Correlation index, 相关指数Correspondence, 对应Counting, 计数Counts, 计数频数Covariance, 协方差Covariant, 共变Cox Regression, Cox回归Criteria for fitting, 拟合准则Criteria of least squares, 最小二乘准则Critical ratio, 临界比Critical region, 拒绝域Critical value, 临界值Cross-over design, 交叉设计Cross-section analysis, 横断面分析Cross-section survey, 横断面调查Crosstabs , 交叉表Cross-tabulation table, 复合表Cube root, 立方根Cumulative distribution function, 分布函数Cumulative probability, 累计概率Curvature, 曲率弯曲Curvature, 曲率Curve fit , 曲线拟和Curve fitting, 曲线拟合Curvilinear regression, 曲线回归Curvilinear relation, 曲线关系Cut-and-try method, 尝试法Cycle, 周期Cyclist, 周期性D test, D检验Data acquisition, 资料收集Data bank, 数据库Data capacity, 数据容量Data deficiencies, 数据缺乏Data handling, 数据处理Data manipulation, 数据处理Data processing, 数据处理Data reduction, 数据缩减Data set, 数据集Data sources, 数据来源Data transformation, 数据变换Data validity, 数据有效性Data-in, 数据输入Data-out, 数据输出Dead time, 停滞期Degree of freedom, 自由度Degree of precision, 精密度Degree of reliability, 可靠性程度Degression, 递减Density function, 密度函数Density of data points, 数据点的密度Dependent variable, 应变量依变量因变量Dependent variable, 因变量Depth, 深度Derivative matrix, 导数矩阵Derivative-free methods, 无导数方法Design, 设计Determinacy, 确定性Determinant, 行列式Determinant, 决定因素Deviation, 离差Deviation from average, 离均差Diagnostic plot, 诊断图Dichotomous variable, 二分变量Differential equation, 微分方程Direct standardization, 直接标准化法Discrete variable, 离散型变量DISCRIMINANT, 判断Discriminant analysis, 判别分析Discriminant coefficient, 判别系数Discriminant function, 判别值Dispersion, 散布分散度Disproportional, 不成比例的Disproportionate sub-class numbers, 不成比例次级组含量Distribution free, 分布无关性免分布Distribution shape, 分布形状Distribution-free method, 任意分布法Distributive laws, 分配律Disturbance, 随机扰动项Dose response curve, 剂量反应曲线Double blind method, 双盲法Double blind trial, 双盲试验Double exponential distribution, 双指数分布Double logarithmic, 双对数Downward rank, 降秩Dual-space plot, 对偶空间图DUD, 无导数方法Duncan's new multiple range method, 新复极差法Duncan新法E-LEffect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Ellipse, 椭圆Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方和Euclidean distance, 欧式距离Event, 事件Event, 事件Exceptional data point, 异常数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验Experimental sampling, 试验抽样Experimental unit, 试验单位Explanatory variable, 说明变量Exploratory data analysis, 探索性数据分析Explore Summarize, 探索-摘要Exponential curve, 指数曲线Exponential growth, 指数式增长EXSMOOTH, 指数平滑方法Extended fit, 扩充拟合Extra parameter, 附加参数Extrapolation, 外推法Extreme observation, 末端观测值Extremes, 极端值极值F distribution, F分布F test, F检验Factor, 因素因子Factor analysis, 因子分析Factor Analysis, 因子分析Factor score, 因子得分Factorial, 阶乘Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fanning, 扇面Fatality rate, 病死率Field investigation, 现场调查Field survey, 现场调查Finite population, 有限总体Finite-sample, 有限样本First derivative, 一阶导数First principal component, 第一主成分First quartile, 第一四分位数Fisher information, 费雪信息量Fitted value, 拟合值Fitting a curve, 曲线拟合Fixed base, 定基Fluctuation, 随机起伏Forecast, 预测Four fold table, 四格表Fourth, 四分点Fraction blow, 左侧比率Fractional error, 相对误差Frequency, 频率Frequency polygon, 频数多边图Frontier point, 界限点Function relationship, 泛函关系Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查GENLOG (Generalized liner models), 广义线性模型Geometric mean, 几何平均数Gini's mean difference, 基尼均差GLM (General liner models), 通用线性模型Goodness of fit, 拟和优度配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误Gross-error sensitivity, 大错敏感度Group averages, 分组平均Grouped data, 分组资料Guessed mean, 假定平均数Half-life, 半衰期Hampel M-estimators, 汉佩尔M估计量Happenstance, 偶然事件Harmonic mean, 调和均数Hazard function, 风险均数Hazard rate, 风险率Heading, 标目Heavy-tailed distribution, 重尾分布Hessian array, 海森立体阵Heterogeneity, 不同质Heterogeneity of variance, 方差不齐Hierarchical classification, 组内分组Hierarchical clustering method, 系统聚类法High-leverage point, 高杠杆率点HILOGLINEAR, 多维列联表的层次对数线性模型Hinge, 折叶点Histogram, 直方图Historical cohort study, 历史性队列研究Holes, 空洞HOMALS, 多重响应分析Homogeneity of variance, 方差齐性Homogeneity test, 齐性检验Huber M-estimators, 休伯M估计量Hyperbola, 双曲线Hypothesis testing, 假设检验Hypothetical universe, 假设总体Impossible event, 不可能事件Independence, 独立性Independent variable, 自变量Index, 指标指数Indirect standardization, 间接标准化法Individual, 个体Inference band, 推断带Infinite population, 无限总体Infinitely great, 无穷大Infinitely small, 无穷小Influence curve, 影响曲线Information capacity, 信息容量Initial condition, 初始条件Initial estimate, 初始估计值Initial level, 最初水平Interaction, 交互作用Interaction terms, 交互作用项Intercept, 截距Interpolation, 内插法Interquartile range, 四分位距Interval estimation, 区间估计Intervals of equal probability, 等概率区间Intrinsic curvature, 固有曲率Invariance, 不变性Inverse matrix, 逆矩阵Inverse probability, 逆概率Inverse sine transformation, 反正弦变换Iteration, 迭代Jacobian determinant, 雅可比行列式Joint distribution function, 分布函数Joint probability, 联合概率Joint probability distribution, 联合概率分布K means method, 逐步聚类法Kaplan-Meier, 评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier图Kendall's rank correlation, Kendall等级相关Kinetic, 动力学Kolmogorov-Smirnove test, 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal及Wallis检验多样本的秩和检验H检验Kurtosis, 峰度Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线相关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 损失函数Low correlation, 低度相关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量M-RMain effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形Multidimensional Scaling (ASCAL), 多维尺度多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复相关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负相关Negative linear correlation, 负线性相关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性相关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal ranges, 正常范围Normal value, 正常值Nuisance parameter, 多余参数讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOV A , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规相关Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Partial correlation, 偏相关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正相关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩协方差Profile trace, 截面迹图Proportion, 比构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差全距Rank correlation, 等级相关Rank sum test, 秩和检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 接受域Regression coefficient, 回归系数Regression sum of square, 回归平方和Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方和Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表S-ZSample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system ), SAS统计软件包Scale, 尺度量表Scatter diagram, 散点图Schematic plot, 示意图简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单相关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Time series, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方和Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Two sided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误α错误Type II error, 二类错误β错误UMVU, 方差一致最小无偏估计简称Unbiased estimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Upper limit, 上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性V ARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转V olume of distribution, 容积W test, W检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验Cochran检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方和Weighting coefficient, 权重系数Weighting method, 加权法W-estimation, W估计量W-estimation of location, 位置W估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法配对符号秩和检验Wild point, 野点狂点Wild value, 野值狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z检验Zero correlation, 零相关Z-transformation, Z变换。
LTE试卷(带答案) 2
LTE培训试卷总分：100分时间：90分钟姓名：___________ 班级：__________模块1 得分_____一、填空题（每空1分共30分）1、作为第四代移动通信的技术标准，LTE网络在空中接口的上行和下行分别用了SC-FDMA和OFDMA的多址技术。
2、核心网称为SAE，主要的网元包括SGW 、PDNGW和MME 。
3、LTE的帧格式分为Type1和Type2两种，其中TYPE2是用于TD-LTE。
4、TD-LTE的特殊子帧包括三个时隙：DWPTS、GP和UPPTS,总长1 ms。
5、根据CP长度不同，LTE的每个RB包含的OFDM符号个数不同，Normal CP配置时，每个RB在时域上包含7 个OFDM符号，而Extended CP配置时，每个RB在时域上包含6 个OFDM符号。
6、影响小区吞吐量主要因素有 MIMO ， ICIC ，分组调度，无线资源，发射功率。
7、物理下行控制/业务公共信道/信号有 PCFICH ， PHICH ， PDCCH ， PDSCH ，PSS/SSS ，和 CRS/DRS ；物理上行控制/业务公共信道/信号有 PRACH， PUCCH ，PUSCH ，和 DMRS/SRS。
8、LTE系统中，完成调度功能的调度器位于e-NodeMAC层。
9、TD-LTE系统物理层中常规CP的长度是4.69µs。
10、TDD频段中，中国规划的39频段的上行工作频段是 1880MHz——1920MHz 。
二、单选题（每题1分共16分）1、LTE标准由哪个组织制定（B）A、ITUB、3GppC、3Gpp2D、IEEE2、一个LTE载波的最大带宽是（C）。
A、5MB、10MC、20MD、40M3、LTE是在如下哪个协议版本中首次发布的？（D）A、R99B、R6C、R7D、R84、哪个协议负责空中接口加密和完整性保护？（A ）A、PDCPB、RLCC、MACD、PHY5、LTE的物理广播信道PBCH承载（ A ）A、MIBB、SIB1C、SIB2D、SIB36、LTE网络中，eNODEB之间可以配置接口，从而实现移动性管理，该接口名称是（ D ）A、S1B、S2C、X1D、X27、TDD LTE可以支持（C ）种上下行配比。
统计学专业英语词汇完整版
Ｃoｎtｉｎｇenｃytａble,列联表
Conｔｏur，边界线
Ｃｏnｔｒibutionrａte，贡献率
Ｃｏｎtroｌ,对照
Ｃoｎｔｒｏlleｄeｘpｅriｍeｎｔs,对照实验
Cｏｎveｎtionaldepｔh,常规深度ﻫCｏｎｖoｌuｔiｏn，卷积ﻫCorrｅｃｔeｄｆａcｔoｒ，校正因子
Daｔaｄefiｃiｅnciｅs,数据缺乏ﻫDaｔahandling,数据处理ﻫDaｔamａｎiｐｕlatiｏｎ，数据处理
Dataprocｅssｉng,数据处理ﻫDataredｕctｉon,数据缩减ﻫDataset,数据集ﻫDataｓources，数据来源
Dａtatransｆｏrｍation,数据变换
Cｏding,编码
Coｅｆｆicｉｅntofcｏntingency,列联系数
Cｏefficｉenｔofdeｔermiｎation,决定系数
Coｅffiｃieｎtofmｕltipｌecorｒｅｌａtiｏn，多重相关系数
Cｏｅfficientofpartialcorrelation,偏相关系数
Coefficieｎtofpｒoductiｏｎ—mｏmentcorrelation,积差相关系数ﻫＣoefficｉentofraｎｋcorrelａtion,等级相关系数ﻫＣoefｆｉｃientofregｒessｉon,回归系数
Ｂ
Barcｈａrt,条形图ﻫBarｇrａph,条形图ﻫBaseperiｏｄ,基期
Baｙestｈeｏrem,贝叶斯定理ﻫBelｌ－sｈａpedｃurｖｅ，钟形曲线ﻫBerｎoullｉdｉｓｔｒibutｉon，伯努力分布
Best-ｔrｉmeｓtimatoｒ,最好切尾估计量ﻫBｉａs,偏性
超级电容器分数阶建模与其控制方法分析
华北电力大学硕士学位论文原创性声明本人郑重声明：此处所提交的硕士学位论文《超级电容器分数阶建模及其控制方法研究》，是本人在导师指导下，在华北电力大学攻读硕士学位期间独立进行研究工作所取得的成果。
据本人所知，论文中除已注明部分外不包含他人已发表或撰写过的研究成果。
对本文的研究工作做出重要贡献的个人和集体，均已在文中以明确方式注明。
本声明的法律结果将完全由本人承担。
作者签名：日期：年月日华北电力大学硕士学位论文使用授权书《超级电容器分数阶建模及其控制方法研究》系本人在华北电力大学攻读硕士学位期间在导师指导下完成的硕士学位论文。
本论文的研究成果归华北电力大学所有，本论文的研究内容不得以其它单位的名义发表。
本人完全了解华北电力大学关于保存、使用学位论文的规定，同意学校保留并向有关部门送交论文的复印件和电子版本，允许论文被查阅和借阅。
本人授权华北电力大学，可以采用影印、缩印或其他复制手段保存论文，可以公布论文的全部或部分内容。
本学位论文属于（请在以上相应方框内打“√”）：保密□，在年解密后适用本授权书不保密□作者签名：日期：年月日导师签名：日期：年月日摘要摘要超级电容器是一种具有发展前景的储能元件，建立其精确的模型对于进一步研究超级电容器的实际应用具有重要的意义。
本文对不同规格的超级电容器的阻抗在不同充电程度下的频率特性进行了测量，对基于超级电容器阻抗的分数阶特性进行了分析。
提出了利用分数阶矢量匹配法进行阻抗拟合，进而建立超级电容器分数阶模型的方法。
综合矢量匹配结果以及超级电容器的经典等效电路和多孔电极理论，并考虑了超级电容器内部的法拉第过程，提出一种新的超级电容器的电路模型。
通过对不同电压下的频域特性的拟合得到了参数与电压的关系，建立了超级电容器分数阶非线性模型。
通过对比模型充放电仿真与实验结果，证明了该模型的准确性。
对于超级电容器分数阶模型的阶跃响应，分别在频域利用了分数阶达尔文粒子群算法进行了基于主导极点法的分数阶PID控制器设计，在时域利用了遗传算法与NCD 优化相结合的方法进行了基于优化算法的分数阶PID控制器设计，控制结果仿真说明了分数阶控制器在超级电容器上的应用是成功的，且在对分数阶系统的控制中分数阶控制器显著优于整数阶控制器。
分数阶傅里叶变换讲解
分数阶傅里叶变换的MATLAB 仿真计算以及几点讨论在Haldun M. Ozaktas 和 Orhan Arikan 等人的论文《Digital computation of the fractional Fourier transform 》中给出了一种快速计算分数阶傅里叶变换的算法， 其MATLAB 计算程序可在.tr/~haldun/fracF.m 上查到。
现在基于该程序，对一方波⎪⎩⎪⎨⎧<=其它,01,1)(t t x 进行计算仿真。
注：网上流传较为广泛的FRFT 计算程序更为简洁，据称也是Haldun M. Ozaktas 和 Orhan Arikan 等人的论文《Digital computation of the fractional Fourier transform 》使用的算法。
但是根据Adhemar Bultheel 和 Hector E. Martnez Sulbaran 的论文《Computation of the Fractional Fourier Transform 》中提到，Ozaktas 等人的分数阶傅里叶变换的计算程序仅有上述网站这一处，而两个程序的计算结果基本相符。
本文使用较为简洁的计算程序，Ozaktas 等人的计算程序在附表中给出。
程序如下：clearclc%构造方波⎪⎩⎪⎨⎧<=其它,01,1)(t t x dt=0.05;T=20;t=-T:dt:T;n=length(t);m=1;for k=1:n;% tt=-36+k;tt=-T+k*dt;if tt>=-m && tt<=mx(k)=1;elsex(k)=0;endend%确定α的值alpha=0.01;p=2*alpha/pi%调用计算函数Fx=frft(x,p);Fx=Fx';Fr=real(Fx);Fi=imag(Fx);A=abs(Fx);figure,subplot(2,2,1);plot(t,Fr,'-',t,Fi,':');title(' α=0.01时的实部和虚部π'); axis([-4,4,-1.5,2]);subplot(2,2,2);plot(t,A,'-');title('α=0.01时的幅值');axis([-4,4,0,2]);分数阶傅里叶变换计算函数如下：function Faf = frft(f, a)% The fast Fractional Fourier Transform% input: f = samples of the signal% a = fractional power% output: Faf = fast Fractional Fourier transformerror(nargchk(2, 2, nargin));f = f(:);N = length(f);shft = rem((0:N-1)+fix(N/2),N)+1;sN = sqrt(N);a = mod(a,4);% do special casesif (a==0), Faf = f; return; end;if (a==2), Faf = flipud(f); return; end;if (a==1), Faf(shft,1) = fft(f(shft))/sN; return; end if (a==3), Faf(shft,1) = ifft(f(shft))*sN; return; end% reduce to interval 0.5 < a < 1.5if (a>2.0), a = a-2; f = flipud(f); endif (a>1.5), a = a-1; f(shft,1) = fft(f(shft))/sN; end if (a<0.5), a = a+1; f(shft,1) = ifft(f(shft))*sN; end% the general case for 0.5 < a < 1.5alpha = a*pi/2;tana2 = tan(alpha/2);sina = sin(alpha);f = [zeros(N-1,1) ; interp(f) ; zeros(N-1,1)];% chirp premultiplicationchrp = exp(-i*pi/N*tana2/4*(-2*N+2:2*N-2)'.^2);f = chrp.*f;% chirp convolutionc = pi/N/sina/4;Faf = fconv(exp(i*c*(-(4*N-4):4*N-4)'.^2),f);Faf = Faf(4*N-3:8*N-7)*sqrt(c/pi);% chirp post multiplicationFaf = chrp.*Faf;% normalizing constantFaf = exp(-i*(1-a)*pi/4)*Faf(N:2:end-N+1);function xint=interp(x)% sinc interpolationN = length(x);y = zeros(2*N-1,1);y(1:2:2*N-1) = x;xint = fconv(y(1:2*N-1), sinc([-(2*N-3):(2*N-3)]'/2)); xint = xint(2*N-2:end-2*N+3);function z = fconv(x,y)% convolution by fftN = length([x(:);y(:)])-1;P = 2^nextpow2(N);z = ifft( fft(x,P) .* fft(y,P));z = z(1:N);从图中可见，当旋转角度0→α时，分数阶Fourier 变换将收敛为方波信号)(t x ；当2πα→时，收敛为c sin 函数。
统计术语中英文对照
统计术语中英文对照[全]Absolute deviation, 绝对离差Absolute number, 绝对数Absolute residuals, 绝对残差Acceleration array, 加速度立体阵Acceleration in an arbitrary direction, 任意方向上的加速度Acceleration normal, 法向加速度Acceleration space dimension, 加速度空间的维数Acceleration tangential, 切向加速度Acceleration vector, 加速度向量Acceptable hypothesis, 可接受假设Accumulation, 累积Accuracy, 准确度Actual frequency, 实际频数Adaptive estimator, 自适应估计量Addition, 相加Addition theorem, 加法定理Additivity, 可加性Adjusted rate, 调整率Adjusted value, 校正值Admissible error, 容许误差Aggregation, 聚集性Alternative hypothesis, 备择假设Among groups, 组间Amounts, 总量Analysis of correlation, 相关分析Analysis of covariance, 协方差分析Analysis of regression, 回归分析Analysis of time series, 时间序列分析Analysis of variance, 方差分析Angular transformation, 角转换ANOVA （analysis of variance）, 方差分析ANOVA Models, 方差分析模型Arcing, 弧/弧旋Arcsine transformation, 反正弦变换Area under the curve, 曲线面积AREG , 评估从一个时间点到下一个时间点回归相关时的误差 ARIMA, 季节和非季节性单变量模型的极大似然估计 Arithmetic grid paper, 算术格纸Arithmetic mean, 算术平均数Arrhenius relation, 艾恩尼斯关系Assessing fit, 拟合的评估Associative laws, 结合律Asymmetric distribution, 非对称分布Asymptotic bias, 渐近偏倚Asymptotic efficiency, 渐近效率Asymptotic variance, 渐近方差Attributable risk, 归因危险度Attribute data, 属性资料Attribution, 属性Autocorrelation, 自相关Autocorrelation of residuals, 残差的自相关Average, 平均数Average confidence interval length, 平均置信区间长度Average growth rate, 平均增长率Bar chart, 条形图Bar graph, 条形图Base period, 基期Bayes' theorem , Bayes定理Bell-shaped curve, 钟形曲线Bernoulli distribution, 伯努力分布Best-trim estimator, 最好切尾估计量Bias, 偏性Binary logistic regression, 二元逻辑斯蒂回归Binomial distribution, 二项分布Bisquare, 双平方Bivariate Correlate, 二变量相关Bivariate normal distribution, 双变量正态分布Bivariate normal population, 双变量正态总体Biweight interval, 双权区间Biweight M-estimator, 双权M估计量Block, 区组/配伍组BMDP(Biomedical computer programs), BMDP统计软件包Boxplots, 箱线图/箱尾图Breakdown bound, 崩溃界/崩溃点Canonical correlation, 典型相关Caption, 纵标目Case-control study, 病例对照研究Categorical variable, 分类变量Catenary, 悬链线Cauchy distribution, 柯西分布Cause-and-effect relationship, 因果关系Cell, 单元Censoring, 终检Center of symmetry, 对称中心Centering and scaling, 中心化和定标Central tendency, 集中趋势Central value, 中心值CHAID -χ2 Automatic Interaction Detector, 卡方自动交互检测Chance, 机遇Chance error, 随机误差Chance variable, 随机变量Characteristic equation, 特征方程Characteristic root, 特征根Characteristic vector, 特征向量Chebshev criterion of fit, 拟合的切比雪夫准则Chernoff faces, 切尔诺夫脸谱图Chi-square test, 卡方检验/χ2检验Choleskey decomposition, 乔洛斯基分解Circle chart, 圆图Class interval, 组距Class mid-value, 组中值Class upper limit, 组上限Classified variable, 分类变量Cluster analysis, 聚类分析Cluster sampling, 整群抽样Code, 代码Coded data, 编码数据Coding, 编码Coefficient of contingency, 列联系数Coefficient of determination, 决定系数Coefficient of multiple correlation, 多重相关系数Coefficient of partial correlation, 偏相关系数Coefficient of production-moment correlation, 积差相关系数Coefficient of rank correlation, 等级相关系数Coefficient of regression, 回归系数Coefficient of skewness, 偏度系数Coefficient of variation, 变异系数Cohort study, 队列研究Column, 列Column effect, 列效应Column factor, 列因素Combination pool, 合并Combinative table, 组合表Common factor, 共性因子Common regression coefficient, 公共回归系数Common value, 共同值Common variance, 公共方差Common variation, 公共变异Communality variance, 共性方差Comparability, 可比性Comparison of bathes, 批比较Comparison value, 比较值Compartment model, 分部模型Compassion, 伸缩Complement of an event, 补事件Complete association, 完全正相关Complete dissociation, 完全不相关Complete statistics, 完备统计量Completely randomized design, 完全随机化设计Composite event, 联合事件Composite events, 复合事件Concavity, 凹性Conditional expectation, 条件期望Conditional likelihood, 条件似然Conditional probability, 条件概率Conditionally linear, 依条件线性Confidence interval, 置信区间Confidence limit, 置信限Confidence lower limit, 置信下限Confidence upper limit, 置信上限Confirmatory Factor Analysis , 验证性因子分析Confirmatory research, 证实性实验研究Confounding factor, 混杂因素Conjoint, 联合分析Consistency, 相合性Consistency check, 一致性检验Consistent asymptotically normal estimate, 相合渐近正态估计Consistent estimate, 相合估计Constrained nonlinear regression, 受约束非线性回归Constraint, 约束Contaminated distribution, 污染分布Contaminated Gausssian, 污染高斯分布Contaminated normal distribution, 污染正态分布Contamination, 污染Contamination model, 污染模型Contingency table, 列联表Contour, 边界线Contribution rate, 贡献率Control, 对照Controlled experiments, 对照实验Conventional depth, 常规深度Convolution, 卷积Corrected factor, 校正因子Corrected mean, 校正均值Correction coefficient, 校正系数Correctness, 正确性Correlation coefficient, 相关系数Correlation index, 相关指数Correspondence, 对应Counting, 计数Counts, 计数/频数Covariance, 协方差Covariant, 共变Cox Regression, Cox回归Criteria for fitting, 拟合准则Criteria of least squares, 最小二乘准则Critical ratio, 临界比Critical region, 拒绝域Critical value, 临界值Cross-over design, 交叉设计Cross-section analysis, 横断面分析Cross-section survey, 横断面调查Crosstabs , 交叉表Cross-tabulation table, 复合表Cube root, 立方根Cumulative distribution function, 分布函数Cumulative probability, 累计概率Curvature, 曲率/弯曲Curvature, 曲率Curve fit , 曲线拟和Curve fitting, 曲线拟合Curvilinear regression, 曲线回归Curvilinear relation, 曲线关系Cut-and-try method, 尝试法Cycle, 周期Cyclist, 周期性D test, D检验Data acquisition, 资料收集Data bank, 数据库Data capacity, 数据容量Data deficiencies, 数据缺乏Data handling, 数据处理Data manipulation, 数据处理Data processing, 数据处理Data reduction, 数据缩减Data set, 数据集Data sources, 数据来源Data transformation, 数据变换Data validity, 数据有效性Data-in, 数据输入Data-out, 数据输出Dead time, 停滞期Degree of freedom, 自由度Degree of precision, 精密度Degree of reliability, 可靠性程度Degression, 递减Density function, 密度函数Density of data points, 数据点的密度Dependent variable, 应变量/依变量/因变量 Dependent variable, 因变量Depth, 深度Derivative matrix, 导数矩阵Derivative-free methods, 无导数方法Design, 设计Determinacy, 确定性Determinant, 行列式Determinant, 决定因素Deviation, 离差Deviation from average, 离均差Diagnostic plot, 诊断图Dichotomous variable, 二分变量Differential equation, 微分方程Direct standardization, 直接标准化法Discrete variable, 离散型变量DISCRIMINANT, 判断Discriminant analysis, 判别分析Discriminant coefficient, 判别系数Discriminant function, 判别值Dispersion, 散布/分散度Disproportional, 不成比例的Disproportionate sub-class numbers, 不成比例次级组含量Distribution free, 分布无关性/免分布Distribution shape, 分布形状Distribution-free method, 任意分布法Distributive laws, 分配律Disturbance, 随机扰动项Dose response curve, 剂量反应曲线Double blind method, 双盲法Double blind trial, 双盲试验Double exponential distribution, 双指数分布Double logarithmic, 双对数Downward rank, 降秩Dual-space plot, 对偶空间图DUD, 无导数方法Duncan's new multiple range method, 新复极差法/Duncan新法Effect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Ellipse, 椭圆Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差/错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方和Euclidean distance, 欧式距离Event, 事件Event, 事件Exceptional data point, 异常数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验Experimental sampling, 试验抽样Experimental unit, 试验单位Explanatory variable, 说明变量Exploratory data analysis, 探索性数据分析Explore Summarize, 探索-摘要Exponential curve, 指数曲线Exponential growth, 指数式增长EXSMOOTH, 指数平滑方法Extended fit, 扩充拟合Extra parameter, 附加参数Extrapolation, 外推法Extreme observation, 末端观测值Extremes, 极端值/极值F distribution, F分布F test, F检验Factor, 因素/因子Factor analysis, 因子分析Factor Analysis, 因子分析Factor score, 因子得分Factorial, 阶乘Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fanning, 扇面Fatality rate, 病死率Field investigation, 现场调查Field survey, 现场调查Finite population, 有限总体Finite-sample, 有限样本First derivative, 一阶导数First principal component, 第一主成分First quartile, 第一四分位数Fisher information, 费雪信息量Fitted value, 拟合值Fitting a curve, 曲线拟合Fixed base, 定基Fluctuation, 随机起伏Forecast, 预测Four fold table, 四格表Fourth, 四分点Fraction blow, 左侧比率Fractional error, 相对误差Frequency, 频率Frequency polygon, 频数多边图Frontier point, 界限点Function relationship, 泛函关系Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布/正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查GENLOG (Generalized liner models), 广义线性模型 Geometric mean, 几何平均数Gini's mean difference, 基尼均差GLM (General liner models), 通用线性模型 Goodness of fit, 拟和优度/配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误Gross-error sensitivity, 大错敏感度Group averages, 分组平均Grouped data, 分组资料Guessed mean, 假定平均数Half-life, 半衰期Hampel M-estimators, 汉佩尔M估计量Happenstance, 偶然事件Harmonic mean, 调和均数Hazard function, 风险均数Hazard rate, 风险率Heading, 标目Heavy-tailed distribution, 重尾分布Hessian array, 海森立体阵Heterogeneity, 不同质Heterogeneity of variance, 方差不齐 Hierarchical classification, 组内分组Hierarchical clustering method, 系统聚类法High-leverage point, 高杠杆率点HILOGLINEAR, 多维列联表的层次对数线性模型Hinge, 折叶点Histogram, 直方图Historical cohort study, 历史性队列研究 Holes, 空洞HOMALS, 多重响应分析Homogeneity of variance, 方差齐性Homogeneity test, 齐性检验Huber M-estimators, 休伯M估计量Hyperbola, 双曲线Hypothesis testing, 假设检验Hypothetical universe, 假设总体Impossible event, 不可能事件Independence, 独立性Independent variable, 自变量Index, 指标/指数Indirect standardization, 间接标准化法Individual, 个体Inference band, 推断带Infinite population, 无限总体Infinitely great, 无穷大Infinitely small, 无穷小Influence curve, 影响曲线Information capacity, 信息容量Initial condition, 初始条件Initial estimate, 初始估计值Initial level, 最初水平Interaction, 交互作用Interaction terms, 交互作用项Intercept, 截距Interpolation, 内插法Interquartile range, 四分位距Interval estimation, 区间估计Intervals of equal probability, 等概率区间Intrinsic curvature, 固有曲率Invariance, 不变性Inverse matrix, 逆矩阵Inverse probability, 逆概率Inverse sine transformation, 反正弦变换Iteration, 迭代Jacobian determinant, 雅可比行列式Joint distribution function, 分布函数Joint probability, 联合概率Joint probability distribution, 联合概率分布K means method, 逐步聚类法Kaplan-Meier, 评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier图Kendall's rank correlation, Kendall等级相关Kinetic, 动力学Kolmogorov-Smirnove test, 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal及Wallis检验/多样本的秩和检验/H检验Kurtosis, 峰度Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线相关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 损失函数Low correlation, 低度相关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量Main effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形Multidimensional Scaling (ASCAL), 多维尺度/多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复相关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负相关Negative linear correlation, 负线性相关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性相关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal ranges, 正常范围Normal value, 正常值Nuisance parameter, 多余参数/讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOVA , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规相关 Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Partial correlation, 偏相关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正相关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩/协方差Profile trace, 截面迹图Proportion, 比/构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图/Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差/全距Rank correlation, 等级相关Rank sum test, 秩和检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 接受域Regression coefficient, 回归系数Regression sum of square, 回归平方和Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方和Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表Sample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system ), SAS统计软件包Scale, 尺度/量表Scatter diagram, 散点图Schematic plot, 示意图/简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型 Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单相关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Time series, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方和Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Two sided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误/α错误Type II error, 二类错误/β错误UMVU, 方差一致最小无偏估计简称Unbiased estimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Upper limit, 上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性VARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转Volume of distribution, 容积W test, W检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验/Cochran检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方和Weighting coefficient, 权重系数Weighting method, 加权法W-estimation, W估计量W-estimation of location, 位置W估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法/配对符号秩和检验Wild point, 野点/狂点Wild value, 野值/狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z检验Zero correlation, 零相关Z-transformation, Z变换。
自动化专业专业外语单词
abound v. 大量存在accelerate v. 加速active network 有源网络ad hoc 尤其,特定地admissible adj. 允许的advent n. 出现aforementioned adj. 上述的airgap = air gap 气隙algebraic equation 代数方程alignment n. 组合alleviate v. 减轻,缓和altitude n. 海拔amortisseur n. 阻尼器amplifier n. 放大器amplify v. 放大amplitude n. 振幅apparatus n. 装置approach n. 途径方法研究aptness n. 恰当arbitrary adj. 任意的argument n. 辐角,相位armature n. 电枢,衔铁,加固arrival angle 入射角arrival point 汇合点assembly n. 装置,构件assumption n. 假设asymmetric adj. 不对称的asymptote n. 渐进线asymptotically stable渐近稳定at rest 处于平衡状态attain v. 达到,实现autonomous adj.自激的bandwidth n. 带宽become adept in 熟练binary adj. 二进制的bipolar adj. 双向的Boolean algebra 布尔代数bound v. 限制break frequency 转折频率breakdown n. 击穿,雪崩breakover n. 导通brush n. 电刷building blocks 积木cage n. 笼子,笼形capacitor n. 电容器carrier n. 载波,载体cascade n., v. 串联characteristic adj. 特性(的)n. 特性曲线characteristicequation特方程circuitry n. 电路closed-loop n. 闭环coefficient n. 系数coil n. 绕组,线圈；v. 盘绕coincide v. 一致common logarithm 常对数complex adj. 复数的n.复数comprise v. 包含conduction n. 导电,传导configuration n. 构造,结构confine v. 限制…范围内conjugate adj. 共轭的constant matrix 常数矩阵constitute v. 构造,组织constraint n. 强迫,约束constraint n. 约束条件continuum n. 连续controllabillity n. 能控性converge v. 集中,汇聚,收敛core n. 铁心corresponding adj. 相应的criteria n. 判据critically damped 临界阻尼crystal n. 晶体cumulative adj. 累积的damp v. 阻尼,减幅,衰减damping n. 阻尼；adj. 阻尼的decay v. 衰减decibel n. 分贝decouple v. 解耦,退耦deduce v. 演绎demagnetization 去磁,退磁denominator n. 分母dependent variable 应变量depict v. 描述derivation n. 导数deteriorate v. 恶化,变坏deterministic adj. 确定的develop v. 导出,引入difference equation 差分方程differential 差别的,微分的differentiate v. 微分diode n. 二极管discrete adj. 离散的distributed 分散的分布的disturbance n. 扰动,干扰domain n. 域,领域dominate v. 支配,使服从dominating pole 主极点dual adj. 双的,对偶的dutyratio 占空比,功率比dynamic response 动态响应eigenvalue n. 特征根elastic adj. 有弹性的electric charge 电荷eliminate v. 消除,对消elongate v. 延长,拉长emf(electromotive force )电动势emitter n. 发射极encircle v. 环绕enclose v. 围绕encompass v. 包含entail v., n. 负担,需要equation 方程even adj. 偶数的excitation n. 激励exponential adj. 指数的extreme adj. 极端的facilitatev. 使容易,促进factor n. 因子；v. 分解因式factored adj. 可分解的feedback n. 反馈fictitious adj. 假想的field winding n. 励磁绕组field-weakening n. 弱磁filter n. 滤波器,滤波final value 终值firing angle 触发角flip-flop n. 触发器force commutated 强制换向forcing frequency 强制频率formulation n. 公式化forward biased 正向偏置fractional adj. 分数的fractional adj. 小数的fundamental n. 基本原理gate n. 门,门电路general form 一般形式generalize v. 一般化,普及generator n. 发生器,发电机geometry 几何学几何形状globally stable 全局稳定gouge v. 挖gross national product 国民生产总值GTO 门极可关断晶闸管guarantee v., n. 保证,担保hardware n. 硬件harmonics n. 谐波holding current 保持电流homogeneous solution 通解horizontally adv. 水平地horsepower n. 功率horsepower n. 马力,功率Hurwitz criterion 赫尔维茨据hybrid n. 混合identify v. 确认,识别,辨识identity n. 一致性,等式igit n. 位数imaginary axis 虚轴implement v. 实现implementation 实现履行impulse v. 冲激in series 串联incidentally adv. 偶然地increment n. 增量indentation n. 缺口independent variable 自变量inductor n. 电感器infinitesimal adj. 无限小的inhibit v. 抑制initial condition 初始条件initial value 初值insofar as 到这样的程度在……范围内integer n. 整数integral / integrate 积分integrated circuit 集成电路intersect v. 相交interval n. 间隔intrinsic adj. 固有的,本征intrinsic adj. 内在的intuition n. 直觉intuitively adv. 直观地inverse transform 反(逆)变换Kirchhoff’s first law 基尔霍夫第一定律lag v., n. 延迟lagging n. 滞后Laplace transformation拉变换lead n. 导线leading adj. 超前的leakage current 漏电流linearazation n. 线性化locally stable 局域稳定loop current 回路电流lumped adj. 集中的magnitude n. 幅值manipulate v. 处理matrix n. 模型,矩阵matrix algebra 矩阵代数mechanize v. 使机械化merit n. 优点；指标,准则mesh n. 网孔minimize v. （使）最小化minimum phase 最小相位misinterpretation 曲解误译model n. 模型v. 建模modification n. 修正,修改multiplication n. 复合性multiply v. 加倍,倍增multivariable adj. 多变量的multivariable n. 多变量n-dimensional n维的net n. 净值；adj. 净值的network n. 网络,电路neutral adj. 中性的；n. 中性线nonlinear adj. 非线性的notch n. 换相点,换级点numerator n. 分子numerical adj. 数字的observability n. 能观性observable adj. 可观测的odd multiple 奇数倍omit v. 省略on the order of 约为open-loop n. 开环optimal control 最优控制order n. 阶origin n. 原点oscillation n. 振荡outline n. 轮廓；v. 提出……的要点overdamped adj. 过阻尼的overshoot n. 超调量,超调package n. 包parallel n. 类似parameter n. 参数partial fraction expansion 部分分式展开式particular solution 特解passive adj. 被动的,无源的passive network 无源网络peak time 峰值时间performance criteria 性能指标performance index 性能指标periodic adj. 周期性的phase n. 状态,相位phase sequence 相序phase-lag n. 相位滞后phase-plane equation相平面方程pilot n. 飞行员plant n. 机器,设备被控对象plot v. 绘图n. 曲线图polar plot 极坐标图polarity n. 极性polynomial n. 多项式portrait n. 描述positive definite 正定potential n. (电)势power factor 功率因数predictable adj. 可断定的predominance n. 优势prevalent adj. 流行的prevent…from doing 使……不……principal adj. 主要的probability theory 概率论procedure n. 程序,过程product n. 乘积property n. 性质proportional to 与…成正比Pulsate v. 脉动,跳动,振动quadrant n. 象限quadratic adj. 二次的；n. 二次方程qualitatively adv. 定性地quasi adj. 近似的radically adv. 完全地radius n. 半径radix n. 权random adj. 随机的rated adj. 额定的,设计的,适用的rationale n. 理论real axis 实轴recovery n. 恢复rectification n. 整流rectifier n. 整流器regulate v. 调整relay n. 继电器relevance n. 关联remainder n. 余数represent v. 代表,表示resistance n. 阻抗resistor n. 电阻器reveal v. 显现,揭示reverse 反转变换极性的reverse biased 反向偏置rheostat n. 变阻器ripple n. 波纹,波动rise time 上升时间rms = root-mean-square 有效值,方均根rotor n. 转子Routh criterion 劳斯判据rugged adj. 结实的,耐用的sampled-data n. 采样数据saturation n. 饱和scalar adj. 数量的,标量的；n.数量,标量scheme n. 方法,形式,示意图schottky diode 肖基特二极管semicircle n. 半圆形semiconductor n. 半导体sensor n. 传感器settling time 调节时间shaft n. 转轴shifting theorem 平移定理shutdown v. 关闭sign n. 符号significance n. 意义simplicity n. 简单simultaneously adv. 同时地sketch v., n. (绘)草图,素描slip n. 转差（率）slop n. 斜率slot n. 槽SMPS 开关电源snubber n. 缓冲器,减震器spatial adj. 空间的spring n. 弹簧square-wave n. 方波stability n. 稳定性startup n. 启动state variable 状态变量state-controllable 状态可控的stationary adj. 静态的stator n. 定子steady-state n. 稳态step n. 阶跃（信号）stepper motor 步进电动机stimulus n. 刺激,鼓励stochastic adj. 随机的straight-forward 直截了当的,简单的strategy n. 方法superposition n. 叠加supersede v. 取代suppress v. 抑制symbolic 符号的,记号的symmetrical adj. 对称的terminology n. 术语threshold n. 门限,阈限,极限thyratron n. 闸流管thyristor n. 晶闸管time-invariant adj. 时不变的tip n. 顶端tolerant adj. 容许的,容忍的trade deficit 贸易赤字trade off 换取trail-and-error n. 试凑法trajectories n. 轨迹,弹道transient adj. 暂态的,瞬态的,过渡的transient response 暂态响应transistor n. 晶体管triangular adj. 三角的turn n. 匝数tutorial adj. 指导性的underdampted 欠阻尼的undergo v. 经历uniform adj. 一致的variable n. 变量vector n. 矢量vertically adv. 垂直地violently adv. 激烈地voltage drop 电压降winding 缠绕的,线圈,绕组with respect to 相对于workhorse n. 重载,重负荷wound-rotor n. 绕线转子yield v. 推导出,得出。
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Abstract We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption. Key words: fractional Fourier transform, discrete random transform, cryptography, image encryption and decryption PACS: 42.30.-d, 42.40.-i, 02.30.Uu
∗ Corresponding author Email address: stliu@ ( Shutian Liu).
Preprint submitted to Optical Communication
6 February 2008
Fourier transform (Gabor transform), however with variable size of the windows [3]. Therefore wavelet transform has been an extremely powerful tool in signal representation in time-frequency joint domain with multi-resolution capability, and has been extensively used in image compression, segmentation, fusion and optical pattern recognitions. The significance of mathematical transforms manifests itself further when the fractional Fourier transform was re-invented in 1980’s [4,5] and became active from 1990’s after its physical interpretations were found in optics [6,7,8]. Actually at the beginning, Namias tried to solve Schr¨ odinger equations in quantum mechanics using fractional Fourier transform as a tool with little notice in community. However, the fractional Fourier transform has found itself in real physical processes of light propagation in a graded index (GRIN) fiber, which is equivalent to a near field diffraction of light, Fresnel diffraction, with a quadratic factor. Thus the fractional Fourier transform can be easily realized in a bulk optical setup consisting of lenses. The fractional Fourier transform provides various of new mathematical operations which are useful in the field of optical information processing. And because fractional Fourier transform also is a kind of time-frequency joint representation of a signal [9], it has found extensive applications in signal and image processing [10]. The discrete forms of mathematical transforms have been extremely useful in applications, especially in signal processing and image manipulations. In fact, discrete transforms can approximate their continuous versions with high precision, meanwhile with high computation speed and lower complexities. Needless to say, Discrete Fourier transform (or FFT) and discrete wavelet transform have been widely used in different kinds of applications. Recently, discrete fractional Fourier transform (DFrFT) and the relevant discrete fractional cosine transform (DFrCT) have been proposed [11,12]. We have used this fast algorithm of fractional Fourier transform in the numerical simulations of image encryption and optical security [13,14]. As we have demonstrated that the extension of fractional Fourier transform have many different kinds of definitions according to how we fractionalize the Fourier transform [15], the DFrFT may also have different kinds of versions. In our researches of optical image encryption, we ask naturally the question, is there any possibility that the DFrFT be random? We have been motivated in searching such a random transform because then the image encryption process could be simplified by a single step of transform. Recently we found that, from the generalization of DFrFT, we can construct a discrete fractional random transform (DFRNT) with an inherent randomness. We demonstrate that such DFRNT has excellent mathematical properties as the fractional Fourier transforms have. And moreover it has some fantastic features of its own. We have also demonstrated that the DFRNT is a very efficient tool in digital image encryption and decryption with a very high speed of computation. The open 2
questions left are concerning with the physical analogies of DFRNT and its further applications, which we are considering now. We discuss the mathematical definition and properties of DFRNT and provide numerical simulation results of the DFRNT’s for one-dimensional and twodimensional signals in the following sections in details.
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Introduction
It is well known that the mathematical transforms from time (or space) to frequency domain or joint time-frequency domain, such as Fourier transform, Winger distribution function, wavelet transform and more recent fractional Fourier transform, etc. have long been powerful mathematical tools in physics and information processing. For instance, Fourier transform has been the basic tool for signal representation, analysis and processing, image processing and pattern recognition. In physics the Fourier transform describes well the Fraunhofer (far field) diffraction of light and thus has been the fundamental of information optics [1]. More recently, in the research of quantum information, Fourier transform algorithm has been adopted as an effective and fundamental algorithm in quantum computer [2]. Wavelet transform is a kind of windowed