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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