 S.1 Prototype adaptive filter  Filter structure  Quadratic cost functions  S2. Wiener filter theory  MMSE criterion  Wiener-Hopf equations  Orthogonality principle  S3. Unrealizable Wiener filter

1. Wiener filter 2. Adaptive Wiener filter

作为炼钢厂的关键设备，风机担负着转炉除尘和煤气回收的重要任务，实现风机剩余使用寿命的准确预测具有重要的实际意义.通过对邯郸某炼钢厂风机振动数据的分析，建立了基于Wiener过程的状态退化模型，在首达时间的意义下，推导出风机剩余使用寿命的概率密度函数的解析表达式，提出了一种基于极大似然估计的参数实时估计方法，从而实现风机剩余使用寿命的在线实时预测.实验结果表明，相对于文献中的方法，本文所提出的预测方法可以得到更高的预测精度和较低的预测不确定性

–匹配滤波器 –Winer最优估计 –Wiener-Hopf方程 –LMS滤波

◆ A Model of the Image Degradation/Restoration Process ◆ Noise Models ◆ Restoration in the Presence of Noise Only-Spatial Filtering ◆ Periodic Noise Reduction by Frequency Domain Filtering ◆ Linear, Position-Invariant Degradations ◆ Estimating the Degradation Function ◆ Inverse Filtering ◆ Minimum Mean Square Error (Wiener) Filtering ◆ Constrained Least Squares Filtering ◆ Geometric Mean Filter ◆ Image Reconstruction from Projections*

一、功率谱密度的定义 二、WienerKhinchin-定理定理4.8(Wiener-Khinchin-定理)若X(t)为宽平稳过程,且其自相关函数Rx()满足

1 Fundamentals of Control Theory N. Wiener: Control theory in engineering, whether it is Concerned with Man, animal or machine, can only be regarded as a part of the theory of information [(G) Controller

Ch. 22 Unit root in Vector Time series 1 Multivariate Wiener Processes and multivari- ate FCLT Section 2.1 of Chapter 21 described univariate standard Brownian motion W(r) as a scalar continuous-time process(W: rE0, 1-R). The variable W(r) has a N(O, r)distribution across realization, and for any given realization, w(r) is continuous function of the date r with independent increments. If a set of k such independent processes, denoted