Multi-Channel Multi-Variate Equalizer Design

Rajagopal, R.; Potter, Lee C.

doi:10.1007/978-1-4757-6342-3_5

Cited by 5 publications

(9 citation statements)

References 20 publications

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“…Their algorithm [14], [16] first computes every maximal minor of H(z) and the corresponding adjoint matrix. Then it uses them to compute an inverse of H(z).…”

Section: Algorithm 1 Particular Polynomial Inversementioning

confidence: 99%

“…Rajagopal and Potter in [14], [16] show that if H(z) is noninvertible and N ≥ P , then the P ×P maximal minors of H(z) have a common zero. Suppose (z 1 /z 0 ,z 2 /z 0 , ...,z M /z 0 ) is a solution of the maximal minors of H(z) wherez 0 = 0.…”

Section: B Generically Invertible When N − P ≥ Mmentioning

confidence: 99%

“…Methods using Gröbner bases techniques for testing the invertibility of and for computing a particular inverse of an N × 1 multivariate polynomial matrix H(z) were proposed in [14], [15]. For an N × P multivariate polynomial matrix H(z) where P > 1, adjoint matrix methods are employed in [14], [16]. Park in [17] provides a method to find the inverse of a Laurent polynomial matrix G(z).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generic Invertibility of Multidimensional FIR Filter Banks and MIMO Systems

Law

Fossum

Minh

2009

IEEE Trans. Signal Process.

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Abstract-We study the invertibility of M -variate Laurent polynomial N × P matrices. Such matrices represent multidimensional systems in various settings such as filter banks, multiple-input multiple-output systems, and multirate systems. Given an N × P Laurent polynomial matrix H (z1, ..., zM ) of degree at most k, we want to find a P × N Laurent polynomial left inverse matrix G(z) of H (z) such that G(z)H (z) = I. We provide computable conditions to test the invertibility and propose algorithms to find a particular inverse.The main result of this paper is to prove that H (z) is generically invertible when N − P ≥ M ; whereas when N − P < M , then H (z) is generically noninvertible. As a result, we propose an algorithm to find a particular inverse of a Laurent polynomial matrix that is faster than current algorithms known to us.

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“…Their algorithm [14], [16] first computes every maximal minor of H(z) and the corresponding adjoint matrix. Then it uses them to compute an inverse of H(z).…”

Section: Algorithm 1 Particular Polynomial Inversementioning

confidence: 99%

Section: B Generically Invertible When N − P ≥ Mmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generic Invertibility of Multidimensional FIR Filter Banks and MIMO Systems

Law

Fossum

Minh

2009

IEEE Trans. Signal Process.

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“…Over the last decade, the theory and applications of multichannel deconvolution have grown rapidly, such as channel equalization for multiple antennas [1], multichannel image deconvolution [2], and polarimetric calibration of radars [3]. In these applications, the original signal is filtered by multiple finite impulse response (FIR) filters with possible additive noise, and the goal of the multichannel deconvolution is to reconstruct the original signal given the multiple filtered signal as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…In general, the resulting filters do not have minimum support. Rajagopal and Potter applied the Gröbner basis to compute equalizers without the prior knowledge of the support of the deconvolution filters [3]. The filters they considered are polynomial or causal filters, while the filters we consider here are general FIR filters.…”

Section: Introductionmentioning

confidence: 99%

Multichannel FIR Exact Deconvolution In Multiple Variables

Zhou

Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.

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We present a general framework for multichannel exact deconvolution with multivariate finite impulse response (FIR) convolution and deconvolution filters using algebraic geometry. Previous work formulates the problem of multichannel FIR deconvolution into that of the left inverse of a convolution matrix which is solved by linear algebra. However, this approach requires the prior information of the support of deconvolution filters. Using algebraic geometry, we find a necessary and sufficient existence condition of FIR deconvolution filters and propose a simple algorithm based on the Gröbner basis to compute deconvolution filters. This computation algorithm obtains deconvolution filters with either minimal order or minimum number of nonzero coefficients, and no prior information of the support is required. Simulation results show that due to the smaller size of deconvolution filters our approach achieves better results than the liner algebra approach under the impulsive noise environment.

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Applications of Gröbner bases to signal and image processing: a survey

Lin

2004

Linear Algebra and its Applications

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This paper is a tutorial and survey paper on the Gröbner bases method and some of its applications in signal and image processing. Although all the results presented in the paper are available in the literature, we give an elementary treatment here, in the hope that it will further bring awareness of and stimulate interest in Gröbner bases among researchers in signal and image processing. We give first a tutorial on Gröbner bases, and then a survey of the design of multidimensional wavelets and filter banks. Applications of Gröbner bases to other areas of signal and image processing are also briefly reviewed.

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Multi-Channel Multi-Variate Equalizer Design

Cited by 5 publications

References 20 publications

Generic Invertibility of Multidimensional FIR Filter Banks and MIMO Systems

Generic Invertibility of Multidimensional FIR Filter Banks and MIMO Systems

Multichannel FIR Exact Deconvolution In Multiple Variables

Applications of Gröbner bases to signal and image processing: a survey

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