Artículos

 

Diseño óptimo de transformadores de Hilbert sin multiplicadores con base en el uso de un subfiltro simple

 

Optimal Design of Multiplierless Hilbert Transformer based on the Use of a Simple Subfilter

 

David E. Troncoso Romero, Miriam G. Cruz Jiménez y Gordana Jovanovic Dolecek

 

Departamento de Electrónica, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Puebla, México. Correo: dtroncoso@inaoep.mx, miriam_gcj@inaoep.mx, gordana@inaoep.mx.

 

Artículo recibido el 29/11/2010.
Aceptado el 07/03/2011.

 

Resumen

Los transformadores de Hilbert altamente selectivos pueden ser diseñados eficientemente mediante el método de Transformación en Frecuencia (Frequency Transformation, FT), donde un bloque básico, formado con dos subfiltros idénticos, es implementado repetidamente. El número de bloques utilizados se obtiene de la longitud de un filtro prototipo. Recientemente se ha utilizado la técnica Segmentación–Intercalamiento (Pipelining–Interleaving, PI) para evitar el uso repetitivo del bloque básico, reduciendo el número de coeficientes requeridos. Sin embargo, el diseño del subfiltro y del filtro prototipo está basado en una búsqueda heurística. En este artículo se presenta el método óptimo para diseñar el subfiltro y el filtro prototipo, minimizando el número de coeficientes. Además, se propone una estructura alternativa que permite utilizar únicamente un subfiltro dentro del bloque básico. Como resultado, el número total de coeficientes es disminuido. Se demuestra con un par de ejemplos que el método de diseño es óptimo, simple y eficiente.

Palabras Clave: Filtros digitales, transformador de Hilbert.

 

Abstract

Very sharp Hilbert transformers can be efficiently designed by using the Frequency Transformation (FT) method, where a basic building block, formed with two identical subfilters, is repeatedly implemented. The number of the building blocks used is obtained from the length of a prototype filter. Recently, the Pipelining–Interleaving (PI) technique has been applied to avoid the repetitive use of the basic building block, reducing the number of required coefficients. However, the design of the subfilter and the prototype filter is based on a heuristic search. In this paper, we present an optimal method to design the subfilter and prototype filter minimizing the number of coefficients. Additionally, an alternative structure, which permits to use a unique subfilter inside the basic building block, is presented. As a result, the total number of coefficients is decreased. Two examples show that the proposed design method is optimal, simple, and efficient.

Keywords: Digital filters, Hilbert transformer.

 

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Referencias

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