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Adaptive Filtering Applications Part 8

Tham khảo tài liệu 'adaptive filtering applications part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 202 Adaptive Filtering Applications contaminated SEP was set to -10 -15 and -20 dB. The last row of Figure 3 sn shows the simulated primary channel SEP signal at -15dB with EEG and WGN. 2.3 Adaptive noise canceller for SEP extraction using mean square estimation The SEP extraction method under the adaptive noise canceller ANC framework derived from the Mean-Square-Error was firstly introduced and evaluated by some of the present authors in Lam et al. 2005 . From the adaptive filter theory Haykin 2001 and the configuration of the ANC shown in Figure 1 the SEP extraction problem can be solved as a linear ANC problem since the FIR adaptive filter is used named as ANC-SEP approach in this study . The commonly used error measure is the Mean-Square-Error MSE defined as jMSE E e2 ri where E . represents the ensemble operator . The minimisation of the MSE results in the Wiener normal equation under some statistically independent and signal wide-sense stationary IVSS assumptions. The optimal solution of Wiener normal equation can be denoted as w n Rt P 3 where p is the cross-correlation vector between s n and r n and R . is the autocorrelation matrix ofrfn which can be written as p E s n r n R E r l r A 4 As discussed in many literatures the well-known least mean squares EMS algorithm is a stochastic gradient based adaptive algorithm to obtain the optimal solution of Jmse- The updating of the adaptive filter coefficient vector can be denoted as Haykin 2001 w n w n-l 2 uimse n r n 4 where films is the stepsize which is one of the most important factors that controls the initial convergence rate and steady state error of the LMS-ANC for SEP extraction. Generally a big stepsize yields rapid convergence but larger steady-state misadjustment error. A small stepsize yields slow convergence but a corresponding smaller steady-state misadjustment error. There exists a theoretical lower and upper bound of the choice of films details can be referred to Haykin 2001 . Usually the choice