Metodología de diseño de filtros digitales basada en estrategias de optimización metaheurística
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Autores
Ramírez Quiroz, Fabio Andrés
Director
Arango Zuluaga, Eliana Isabel (Thesis advisor)
Tipo de contenido
Trabajo de grado - Maestría
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EspañolFecha de publicación
2017-12-16
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Resumen
En el presente documento se exponen los resultados y productos de la tesis de investigación necesaria para la acreditación del título de Magister en Ingeniería – Ingeniería Eléctrica, otorgado por la Universidad Nacional de Colombia. La investigación estuvo dirigida a proponer, desarrollar e implementar un método de diseño de filtros digitales lineales e invariantes en el tiempo, FIR (Finite Impulse Response) e IIR (Infinite Impulse Response), que considere la cuantificación de los coeficientes del filtro desde el comienzo del proceso de diseño, y no al final, como ocurre en otras metodologías, incluidas las metodologías tradicionales, en las cuales, dicha acción puede incrementar el error de aproximación al filtro deseado, hasta la inestabilidad. Las metodologías de diseño propuestas se basan en los algoritmos de optimización metaheurística APBIL (Adaptive Population-Based Incremental Learning), GA (Genetic Algorithm) y TS (Tabu Search), y están orientadas a obtener la combinación de los coeficientes que mejor se aproxime a la respuesta en frecuencia deseada, para las representaciones binarias de punto fijo (complemento a dos) y punto flotante (según el estándar IEEE 754). Los resultados de las simulaciones son prometedores y muestran un buen desempeño de los filtros obtenidos (destacando el uso del algoritmo APBIL), en términos del Error Medio Cuadrático entre las respuestas en frecuencia deseada y la obtenida a partir de filtro optimizado. Como resultado, se construyó un software amigable, capaz de proporcionar diseños competentes, que logran superar en calidad a los diseños tradicionales, especialmente si el número de coeficientes y/o la precisión numérica son limitados.
This document presents the results and products of the research thesis for the accreditation of the Magister’s degree in Engineering –Electrical Engineering, granted by the National University of Colombia. The research was aimed at proposing, developing and implementing a method of designing linear and time - invariant digital filters, FIR (Finite Impulse Response) and IIR (Infinite Impulse Response), which considers the quantification of digital filter coefficients since the beginning of the design process, and not at the end, as in others methodologies, including the traditional methodologies, in them this action might increase the approach error to the desired filter, un til the instability. The proposed design methodologies are based on APBIL ( Adaptive Population-Based In cremental Learning), GA (Genetic Algorithm) and TS (Tabu Search) metaheurisitc optimization algorithms, and are oriented to obtain the combination of coefficients that best approximates the response at desired frequency, for fixed point (two’s complement) and floating point (according to Std IEEE 754) binary representations. The results of the simulations are promising and show a good performance of the o btained filters (highlighting the use of the APBIL alg orithm), in terms of the Mean Squared Error between the desired frequency response and that oained from the optimized. filter. As a result, a user - friendly software has been built to provide competent designs that are able to outperform traditional designs, especially when number of coefficients and/or numerical precision are limited
This document presents the results and products of the research thesis for the accreditation of the Magister’s degree in Engineering –Electrical Engineering, granted by the National University of Colombia. The research was aimed at proposing, developing and implementing a method of designing linear and time - invariant digital filters, FIR (Finite Impulse Response) and IIR (Infinite Impulse Response), which considers the quantification of digital filter coefficients since the beginning of the design process, and not at the end, as in others methodologies, including the traditional methodologies, in them this action might increase the approach error to the desired filter, un til the instability. The proposed design methodologies are based on APBIL ( Adaptive Population-Based In cremental Learning), GA (Genetic Algorithm) and TS (Tabu Search) metaheurisitc optimization algorithms, and are oriented to obtain the combination of coefficients that best approximates the response at desired frequency, for fixed point (two’s complement) and floating point (according to Std IEEE 754) binary representations. The results of the simulations are promising and show a good performance of the o btained filters (highlighting the use of the APBIL alg orithm), in terms of the Mean Squared Error between the desired frequency response and that oained from the optimized. filter. As a result, a user - friendly software has been built to provide competent designs that are able to outperform traditional designs, especially when number of coefficients and/or numerical precision are limited
Abstract
Palabras clave
filtros digitales ; cuantificación ; procesamiento digital de señales ; Aprendizaje Incremental Basado en Poblaciones ; Algoritmos Genéticos ; Búsqueda Tabú ; diseño óptimo ; Population-Based Incremental Learning ; Genetic Algorithm ; Tabu Search, ; Optimal design ; Digital filter ; Quantification ; Digital processing signal