DSPCIS Chapter13 Least Mean Squares LMS Algorithm Marc

Part-III : Optimal & Adaptive Filters Chapter-11 : Optimal & Adaptive Filters - Intro

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm (Widrow 1965 !!) DSP-CIS / Chapter-13 : Least Mean

Least Mean Squares (LMS) Algorithm Bernard Widrow https: //www. youtube. com/watch? v=hc 2 Zj

Least Mean Squares (LMS) Algorithm large λ_max implies a small stepsize DSP-CIS / Chapter-13

Least Mean Squares (LMS) Algorithm error vector projected onto eigenvectors initial error vector projected

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean

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DSP-CIS Chapter-13: Least Mean Squares (LMS) Algorithm Marc Moonen Dept. E. E. /ESAT-STADIUS, KU Leuven marc. moonen@esat. kuleuven. be www. esat. kuleuven. be/stadius/

Part-III : Optimal & Adaptive Filters Chapter-11 : Optimal & Adaptive Filters - Intro • General Set-Up • Applications • Optimal (Wiener) Filters – : Least Squares & Recursive Least Squares Estimation Chapter-12 • Least Squares Estimation • Recursive Least Squares (RLS) Estimation • Square-Root Algorithms – : Least Means Squares (LMS) Algorithm Chapter-13 • LMS/NLMS : Stochastic Gradient Algorithms • LMS analysis • LMS Family Chapter-14 – : Fast Recursive Least Squares Algorithms Chapter-15 : Kalman Filtering DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 2

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 3

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 4

Least Mean Squares (LMS) Algorithm (Widrow 1965 !!) DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 5

Least Mean Squares (LMS) Algorithm Bernard Widrow https: //www. youtube. com/watch? v=hc 2 Zj 55 j 1 z. U DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 6

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 7

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 8

Least Mean Squares (LMS) Algorithm large λ_max implies a small stepsize DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 9

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 10

Least Mean Squares (LMS) Algorithm error vector projected onto eigenvectors initial error vector projected onto eigenvectors (=projection on i-th eigenvector) DSP-CIS small λ_i implies slow convergence / Chapter-13 Mean Squares (LMS)small Algorithm Version 2014 -2015 λ_min: Least <<λ_max (hence μ) /implies *very* slow convergence p. 11

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 12

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 13

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 14

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 15

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 16

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 17

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 18

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 19

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 20

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 21

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 22

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 23

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 24

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 25

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 26

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 27

Skip this slide Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 28

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 29

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 30

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 31

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 32

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 33

Least Mean Squares (LMS) Algorithm DSP-CIS / Chapter-13 : Least Mean Squares (LMS) Algorithm / Version 2014 -2015 p. 34