"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 6, 2016

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Computing coefficients of nonorthogonal Meixner filters with GNU Octave

 

I. M. Kulikovskikh

Samara National Research University, Samara

 

The paper is received on April 17, after correction - on May 20, 2016

Abstract. Previous research indicates that the Meixner filters can be a constructive alternative to the discrete Laguerre filters in signal processing applications. This may be explained by the impact of an extra parameter which allows providing better series expansion: it becomes possible to ensure the same approximation results using fewer terms. However, the orthogonal Meixner filters extensively studied so far either 1) have a rational z-transform only for even values of the extra parameter or 2) suggest synthesizing the Meixner filters from the Laguerre filters based on matrices transformation that leads to hardware redundancy. The primary focus of the present study is the nonorthogonal Meixner filters. In contrast to the previously discussed filters, these filters are rational for any integer value of the extra parameter and have a simple structure. But, it still seems that more attention needs to be drawn to the problem of expansions in nonorthogonal filters. This paper is aimed at considering the problem of computing the coefficients of the nonorthogonal Meixner filters with GNU Octave. To achieve this purpose, the study provides the analysis of computing the coefficients using build-in functions: quad, quadgk, quadcc, quadv as well as the vectorized representation of quadl. Based on the analysis results, the present research yields another vectorized representation of the coefficients in the form of normal equation to boost computational efficiency and to ensure numerical stability. In addition, the results of computations experiments confirmed the validity of the proposed vectorized representation to solve pole position problem for the nonorthogonal Meixner filters.

Key words: Meixner filters, vectorized computation, normal equation, quadrature.

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