# Performance Analysis of gradient decent adaptive filters for noise cancellation in Signal Processing

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3 in figures, which shows the error signal, amplitudes of actualization coefficients and transmission characteristics of adaptive filtering algorithms based noise cancellers. 3.1 Different signals of RLS Fig(4): Fast Block LMS 2.5 RLS Algorithm: Recursive least squares (RLS) algorithms exhibit faster convergence speed, and do not have the eigen value spread problem. However, RLS algorithms involve more complicated mathematical operations and require more computational resources than LMS algorithms. RLS algorithm performs the following operations to update the coefficients of an adaptive filter. 1. Calculates the error signal e(n) by using the equation no.(2) as e(n) = d(n) y(n). 2. Updates the filter coefficients by using the following equation: (n)+e(n). (n)..(8) Fig (5): shows input signal, signal+ noise signal, output signal, error signal 3.2 Different signals of NLMS where is the filter coefficients vector and is the gain vector. is defined by the following equation:.(9) where λ is the forgetting factor and P(n) is the inverse correlation matrix of the input signal.[adaptive signal theory] P(n) has the following initial value P(0): p(0)= Fig(6): shows input, signal +noise, output & error signal of normalized LMS 3.3 Actualization cofficients of various filtering algorithm where δ is the regularization factor. The standard RLS algorithm uses the following equation to update this inverse correlation matrix. (10). III. SIMULATION RESULTS AND DISCUSSION In this section, test results of various noise cancellation systems simulated in MATLAB are presented. The performance comparison is presented DOI: / P a g e

4 3.3.4 Normalized LMS & RLS 3.3.1Standard LMS 3.4 Error signals of various adaptive filtering algorithms RLS & Signum-signum LMS Fast Block LMS Signum-signum LMS Fast Block LMS DOI: / P a g e

5 3.4.3 LMS & RLS Signum-signum LMS 3.5 Transmission characterstics of different adaptive algorithms Signum-Signum LMS RLS & Normalized LMS Fast Block LMS LMS From the simulation results it can be seen that NLMS perform better than LMS whereas the merits of LMS is memory and number of computational operations requirement is less. It has been observed that there is always tradeoff between step size and MSE, the capability of noise cancellation depends on the number of samples taken into consideration. Fast Block LMS is designed to provide similar performance to the standard LMS algorithm while reducing the computational complexity. Simulation shows that Fast Block LMS offer comparable performance with respect to standard LMS and RLS in addition to a large reduction in computation time for higher order filters, Signum Signum LMS algorithm involve very less DOI: / P a g e

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