Análise de algoritmos para filtragem adaptativa baseados em momentos de quarta ordem [thesis]

Vitor Heloiz Nascimento
À minha família: Naomi, Benedicto, Magdalena e Carlos. AGRADECIMENTOS Aos meus colegas do LPS pelo apoio: Miguel, Denise, Flavio e Mario. Ao Prof. José Bermudez, pela colaboração que deu origem a este trabalho. Ao Prof. Luiz de Queiroz Orsini, pela orientação ao longo desses anos todos. Aos amigos Normonds Alens e Max Gerken, que não chegaram a ver este trabalho. ABSTRACT This dissertation presents a new model for two adaptive filtering algorithms based on fourth-order moments: the least-mean
more » ... s: the least-mean fourth (LMF) and the leastmean mixed-norm (LMMN) algorithms. The novelty of the new model is its emphasis on computing the probability of a reasonable performance of a single realization of the algorithm (in this case, convergence), instead of looking for average performance indices such as mean-square error. We show that the least-mean fourth (LMF) adaptive algorithm is not meansquare stable when the regressor input is not strictly bounded (as happens, for example, if the input has a Gaussian distribution). For input distributions with infinite support, even for the Gaussian distribution, the LMF has always a nonzero probability of divergence, no matter how small the step-size is chosen. We prove this result for a slight modification of the Gaussian distribution in an one-tap filter, and corroborate our findings with several simulations.
doi:10.11606/t.3.2017.tde-23092017-134618 fatcat:pns343wcczbyrni7ptzvw3pep4