Estudio comparativo de los algoritmos de filtrado adaptativo (lms,nlms,rls) para la eliminación del ruido audible externo en tiempo real

Abstract

Adaptive filtering is an algorithm that is applied to a signal of interest contaminated by another undesirable signal and whose purpose is to recover said signal of interest, eliminating that contaminating signal. This is achieved through the use of digital filters whose coefficients or weights are automatically reset by means of Adaptation Algorithms that achieve that in each iteration the error existing between the original signal and the recovered signal is reduced more and more. This work shows a study of the Least Mean Square (LMS), Normalized Least Mean Square (NLMS) and Recursive Least Square (RLS) Adaptive Algorithms in order to select the best of these for real-time application. Also a study of the mathematical formulations of these algorithms that allow their simulation both in time are analyzed Deferred as in real time. After this analysis and implementation, it was determined that the best of the algorithms, in terms of computational load and total error of the samples, is the NLMS. Consequently, it was implemented in real time by Simulink. Although these algorithms can be used in countless applications, the application implemented in this work has to do with the case of Disc Jockeys (DJ) located in the noisy atmosphere of a party, where this DJ tries to listen in his headphones only the next song to be played, eliminating that noisy signal.