Multidimensional FIR filter bank design using Grobner bases

Charoenlarpnopparut, Chalie; Bose, N.K.

doi:10.1109/82.809533

Cited by 62 publications

(52 citation statements)

References 9 publications

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“…By making use of G rrbner bases [5] for modules, Bose and Charoenlarpnopparut have proposed an algorithm for carrying out the zero prime factorization for nD polynomial matrices whose reduced minors are devoid of any common zeros [4], [6]. Lin conjectured that the absence of any common zeros in the reduced minors is a sufficient condition tot the existence of zero prime factorization and also provided a partial solution to this conjecture [18].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, some progress has been made in solving the zero prime factorization problem for nD polynomial matrices [4], [6], [18]. By making use of G rrbner bases [5] for modules, Bose and Charoenlarpnopparut have proposed an algorithm for carrying out the zero prime factorization for nD polynomial matrices whose reduced minors are devoid of any common zeros [4], [6].…”

Section: Introductionmentioning

confidence: 99%

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Factorizations fornD polynomial matrices

Lin

Jin

2001

Circuits Systems and Signal Process

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Abstract. In this paper, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a given nD (n > 2) polynomial matrix whose maximal order minors satisfy certain conditions. It is shown that three classes of nD polynomial matrices admit this kind of general matrix factorization. It turns out that minor prime factorization and determinantal factorization are two interesting special cases of the proposal general factorization. As a consequence, the paper provides a partial solution to an open problem of minor prime factorization as well as to a recent conjecture on minor prime factorizability for nD polynomial matrices. Three illustrative examples are worked out in detail.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Factorizations fornD polynomial matrices

Lin

Jin

2001

Circuits Systems and Signal Process

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“…(An m-variate polynomial matrix G is minor prime 21 , if all maximum-size minors (major determinants) are devoid of common factor other than units.) For a Laurent polynomial ring, the existence condition 8 is relaxed to the condition that the generator matrix must be left factor prime.…”

Section: Propositionmentioning

confidence: 99%

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Charoenlarpnopparut¹

2009

ScienceAsia

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ABSTRACT:Over the past few years, multidimensional convolutional code has become an emerging area of research in the signal processing community. While one-dimensional convolutional code and its variants have been thoroughly understood, the m-D counterpart still lacks unified notation and efficient encoding/decoding implementation. Here, the strong link between the theory of Gröbner bases and m-D convolutional code is explored. Several applications of Gröbner bases to the characterization of m-D convolutional encoders are proposed. Furthermore, the more practical problem of minimal encoder realization is discussed and an algebraic algorithm based on the use of Gröbner bases is provided. From the implementation point of view, the syndrome decoder is currently the only means for decoding m-D convolutional code. A constructive method for computing the syndrome decoding matrix using the theory of syzygy modules is proposed.

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“…The goal is to find synthesis filters such that the system remains a perfect reconstruction for any input discrete signal [12], [13], [14], [15], [16], [17]. In this paper, we consider that the analysis filters are given, but the sampling matrix is unknown.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional Filter Bank Signal Reconstruction From Multichannel Acquisition

Law

Minh

2011

IEEE Trans. on Image Process.

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Abstract-We study the theory and algorithms of an optimal use of multidimensional signal reconstruction from multichannel acquisition by using a filter bank setup. Suppose that we have an N -channel convolution system, referred to as N analysis filters, in M dimensions. Instead of taking all the data and applying multichannel deconvolution, we first reduce the collected data set by an integer M × M uniform sampling matrix D, and then search for a synthesis polyphase matrix which could perfectly reconstruct any input discrete signal. First, we determine the existence of perfect reconstruction (PR) systems for a given set of finite impulse response (FIR) analysis filters. Second, we present an efficient algorithm to find a sampling matrix with maximum sampling rate and to find a FIR PR synthesis polyphase matrix for a given set of FIR analysis filters. Finally, once a particular FIR PR synthesis polyphase matrix is found, we can characterize all FIR PR synthesis matrices, and then find an optimal one according to design criteria including robust reconstruction in the presence of noise.

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Multidimensional FIR filter bank design using Grobner bases

Cited by 62 publications

References 9 publications

Factorizations fornD polynomial matrices

Factorizations fornD polynomial matrices

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Multidimensional Filter Bank Signal Reconstruction From Multichannel Acquisition

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