Synthesis of separable-denominator multidimensional digital lattice filters

Eiji Watanabe, Akinori Nishihara

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Digital filters play an important role in multidimensional signal processing. Because the coefficients must be expressed in finite wordlength, the deterioration of the characteristics becomes a problem. Using a lattice structure whose efficiency has been confirmed for one-dimensional (1-D) digital filters, this paper proposes a unified synthesis method for the practically important separable-denominator multidimensional IIR digital filters. First, the implementation of a 2-D separable-denominator transfer function by a separable-denominator 2-D digital lattice filter is considered. A characteristic of the proposed separable-denominator 2-D digital lattice filter is that both the usual tapped lattice structure and the injection-type lattice structure are used and the signal flow becomes simple compared to the method so far. Next, when the numerator polynomial is a mirror-image polynomial, an implementation method is presented in which the number of tap multipliers is reduced significantly. Furthermore, a method is suggested for the synthesis of a 3-D transfer function based on the same approach as for the 2-D case. Finally, the efficiency of this method is confirmed by an example.

Original languageEnglish
Pages (from-to)97-105
Number of pages9
JournalElectronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
Volume77
Issue number3
Publication statusPublished - 1994 Mar

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Digital filters
Transfer functions
Polynomials
IIR filters
Deterioration
Signal processing
Mirrors

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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abstract = "Digital filters play an important role in multidimensional signal processing. Because the coefficients must be expressed in finite wordlength, the deterioration of the characteristics becomes a problem. Using a lattice structure whose efficiency has been confirmed for one-dimensional (1-D) digital filters, this paper proposes a unified synthesis method for the practically important separable-denominator multidimensional IIR digital filters. First, the implementation of a 2-D separable-denominator transfer function by a separable-denominator 2-D digital lattice filter is considered. A characteristic of the proposed separable-denominator 2-D digital lattice filter is that both the usual tapped lattice structure and the injection-type lattice structure are used and the signal flow becomes simple compared to the method so far. Next, when the numerator polynomial is a mirror-image polynomial, an implementation method is presented in which the number of tap multipliers is reduced significantly. Furthermore, a method is suggested for the synthesis of a 3-D transfer function based on the same approach as for the 2-D case. Finally, the efficiency of this method is confirmed by an example.",
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N2 - Digital filters play an important role in multidimensional signal processing. Because the coefficients must be expressed in finite wordlength, the deterioration of the characteristics becomes a problem. Using a lattice structure whose efficiency has been confirmed for one-dimensional (1-D) digital filters, this paper proposes a unified synthesis method for the practically important separable-denominator multidimensional IIR digital filters. First, the implementation of a 2-D separable-denominator transfer function by a separable-denominator 2-D digital lattice filter is considered. A characteristic of the proposed separable-denominator 2-D digital lattice filter is that both the usual tapped lattice structure and the injection-type lattice structure are used and the signal flow becomes simple compared to the method so far. Next, when the numerator polynomial is a mirror-image polynomial, an implementation method is presented in which the number of tap multipliers is reduced significantly. Furthermore, a method is suggested for the synthesis of a 3-D transfer function based on the same approach as for the 2-D case. Finally, the efficiency of this method is confirmed by an example.

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