DSP-CIS Chapter-12: Least Mean Squares (LMS) Algorithm

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Presentation transcript:

DSP-CIS Chapter-12: Least Mean Squares (LMS) Algorithm Marc Moonen Dept. E.E./ESAT, KU Leuven marc.moonen@esat.kuleuven.be www.esat.kuleuven.be/scd/

Part-III : Optimal & Adaptive Filters Chapter-11 : Optimal & Adaptive Filters - Intro General Set-Up Applications Optimal (Wiener) Filters : Least Squares & Recursive Least Squares Estimation Least Squares Estimation Recursive Least Squares (RLS) Estimation Square-Root Algorithms : Least Means Squares (LMS) Algorithm LMS/NLMS : Stochastic Gradient Algorithms LMS analysis LMS Family : Fast Recursive Least Squares Algorithms : Kalman Filtering Chapter-12 Chapter-13 Chapter-14 Chapter-15

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm (Widrow 1965 !!)

Least Mean Squares (LMS) Algorithm Bernard Widrow

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm  large λ_max implies a small stepsize

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm error vector projected onto eigenvectors initial error vector projected onto eigenvectors (=projection on i-th eigenvector) small λ_i implies slow convergence λ_min <<λ_max (hence small μ) implies *very* slow convergence

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm

Least Mean Squares (LMS) Algorithm