Análise do efeito da precisão finita no algoritmo adaptativo sigmoidal

• Ano de defesa: 2017
• Autor(a) principal: Fonseca, José de Ribamar Silva
• Orientador(a): BARROS FILHO, Allan Kardec Duailibe
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Maranhão
• Programa de Pós-Graduação: PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA DE ELETRICIDADE/CCET
• Departamento: DEPARTAMENTO DE ENGENHARIA DA ELETRICIDADE/CCET
• País: Brasil
• Palavras-chave em Português: Filtros Adaptativos; Quantização; Aritmética de Ponto-Fixo
• Palavras-chave em Inglês: Sigmoidal; Adaptive Filters; Quantization; Fixed-Point Arithmetic
• Área do conhecimento CNPq: Matemática da Computação
• Link de acesso: http://tedebc.ufma.br:8080/jspui/handle/tede/1742

The adaptive filtering is currently an important tool in the statistical processing of signals, especially when it is necessary to process signals from environments with unknown statistics varying with time. The adaptive filtering study was driven by the development of the Least Mean Square algorithm (LMS) in 1960. Since then other adaptive algorithms have come up with a better performance than LMS algorithm with respect to misadjustment and convergence rate. Among them, the Sigmoidal algorithm (SA) which showed superior to the LMS, for the convergence rate and the mismatch in their implementations infinite precision. In hardware devices such as DSPs, microcontrollers and FPGAs, adaptive algorithms are implemented in finite precision, in general, fixed point arithmetic. When the adaptive filters are implemented in finite precision some effects can affect their performance. Ultimately lead to divergence due to quantization errors specified in the approximation process of the variables involved in the adaptive processing of their original values. Thus, this article aims to analyze the performance of the adaptive algorithm Sigmoidal (SA) in finite precision when implemented using fixed-point arithmetic. In particular, the analysis of its performance curve and mismatch, comparing them in different word lengths (number of bits). The results presented in this article proposes a series of Taylor Ln gradient of cost function (cosh αe) algorithm SA for implementation in finite precision. We analyze its performance curve for different lengths of words. It shows that the algorithm is stable in its performance compared to convergence to different lengths of words, and that the increase in mismatch level at steady state is sensitive or afected by the quantization of the variables involved in the calculations of this algorithm.