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Unformatted text preview: SIMULATION OF RLS AND LMS ALGORITHMS FOR ADAPTIVE NOISE CANCELLATION IN MATLAB. J., Oravec R., Kadlec J., Cocherová E. Department of Radioelectronics, FEI STU Bratislava, Slovak Republic UTIA, CAS Praha, Czech Republic Abstract : The main goal of this article is to describe different algorithms of adaptive filtering, mainly the RLS and LMS algorithm, to perform simulation these algorithms in MATLAB - SIMULINK and finally, compare these algorithms. DESCRIPTION: To compare the RLS and LMS algorithms we utilised and improved the existing functional scheme from MATLAB, precisely the scheme of RLS and LMS algorithms for adaptive noise cancellation, as is shown in the Figures 2-4. The subfigure in the Fig.2 stayed without changes, while the internal parts of schemes of RLS adaptive filters (Fig. 4, on the left) and of LMS adaptive filters (Fig. 4, on the left) we changed radically. The all scheme, as is shown in the Fig. 4, is represented by one block, i.e. the block of matlab-function. Since every matlab-function has only one input, we insert a multiplexer, which all the input signals collects to the one vector. Fig. 1. Block diagrams of noise cancellation LMS algorithm (on left) and RLS algorithm (on right) Fig. 2. Sub-scheme of adaptive filters LMS (on left) and RLS (on right) Fig. 3. Detailed diagrams of adaptive filters LMS (on left) a RLS (on right) Fig. 4. Adaptive LMS filter (on left), adaptive RLS filter (on right) We based the algorithms development on the equations (1) and (2), which describe the evaluation of filter coefficients in following way: ( 29 [ ] ( 29 [ ] ( 29 [ ] ( 29 [ ] ( 29 [ ] 1 1 1 1 1 1 1 1 1 1 1 +- +- + +--- +- = + k uu T k uu T k k uu uu uu k X k X k X k X k X u u u u (1) ( 29 ( 29 ( 29 [ ] ( 29 ( 29 1 1 Pr 1 1 1 1 1 1 + + + + +-- ⋅ + + = + k k zvyšok ioritný LS T k k vektor Kalman k uu LS LS k d k X k k ε w u u w w k (2) These relations we rewrite to the form of m-file as a file rls1.m : 1 function y=rls1 (u); 2 global Wo Wn Wm Po Pn Pm; 3 [m,n]=size(u);...
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