Lecture 3 Adaptive Wiener and Biomedical Applications Contents in the lecture: 1.Wiener filter 2.Adaptive Wiener filter 1
1 Lecture 3 Adaptive Wiener and Biomedical Applications Contents in the lecture: 1. Wiener filter 2. Adaptive Wiener filter
1.Wiener filter Reviewing Wiener filter 2
1. Wiener filter Reviewing Wiener filter 2
2.Adaptive Wiener Filter (AWF) Introduction The features of Wiener Filter: (1)Be suitable to process stationary random signals (2)The prior statistical properties for signals and noise is required (3)The parameters of filter system are fixed 3
3 2. Adaptive Wiener Filter (AWF) Introduction The features of Wiener Filter: (1) Be suitable to process stationary random signals (2) The prior statistical properties for signals and noise is required (3) The parameters of filter system are fixed
Introduction Kalman Filtering (1)be suitable to process non-stationary random signals; (2)The prior statistical properties for signals and noise are required; (3)The parameters of the filter are time variation. 4
4 Introduction Kalman Filtering （ 1 ）be suitable to process non-stationary random signals； （ 2 ）The prior statistical properties for signals and noise are required; （ 3 ）The parameters of the filter are time – variation
Introduction Biomedical signal analysis in practice (1)The complexity and non-stationary of biomedical signals; (2)Be impossible to obtain the prior information of signals and noise;Or (3)The statistical properties vary with time. Therefore,Wiener filter and Kaleman filter can not realize the optimum filtering in above situations. However,Adaptive filter can provide the excellent filtering performances. 5
5 Introduction Biomedical signal analysis in practice (1) The complexity and non-stationary of biomedical signals; (2) Be impossible to obtain the prior information of signals and noise; Or (3) The statistical properties vary with time. Therefore, Wiener filter and Kaleman filter can not realize the optimum filtering in above situations. However, Adaptive filter can provide the excellent filtering performances
Introduction Adaptive filter concept By means of the known filter parameters of the previous time,update the filter parameters of the 9( current time to be suitable to the e unknown statistical properties of signals a and noise for the optimum filter. 6
6 Introduction Adaptive filter concept By means of the known filter parameters of the previous time, update the filter parameters of the current time to be suitable to the unknown statistical properties of signals and noise for the optimum filter
Several main adaptive filters (1)LMS adaptive filter(闭环结构) (2)RLS (Recursive least-squares) adaptive filter （开环结构） (3)IIR adaptive filter ■■■■■ 7
7 Several main adaptive filters (1) LMS adaptive filter ( 闭 环 结 构 ） (2) RLS (Recursive least – squares) adaptive filter （ 开 环 结 构 ） (3) IIR adaptive filter 2222
Main applications of AWF Adaptive Noise Canceling Adaptive line enhance 8
8 Main applications of AWF Adaptive Noise Canceling Adaptive line enhance
LMS adaptive Wiener filter The LMS adaptive Wiener filter consists of two basic processes: (1)A filtering process (a.input-output; b.an estimation error)Wiener filtering (2)An adaptive process (the automatic adjustment of the parameters of the filter in accordance with the estimation error) 9
9 LMS adaptive Wiener filter The LMS adaptive Wiener filter consists of two basic processes: (1) A filtering process (a. input–output; b. an estimation error) Wiener filtering (2) An adaptive process (the automatic adjustment of the parameters of the filter in accordance with the estimation error)
LMS adaptive Wiener filter 1 Filtering processing (Wiener filter) Adaptive linear components: x(k-1) 砀 x(k-2 () : x(-0 E() d() 10
10 LMS adaptive Wiener filter Adaptive linear components: 1 Filtering processing （Wiener filter)
