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sankar basu

Bio: sankar basu is an academic researcher. The author has contributed to research in topics: Filter (signal processing) & Filter design. The author has an hindex of 1, co-authored 1 publications receiving 30 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors view the current status of multi-dimensional filters bank and wavelet design from the perspective of signal and system theory, and provide a flavor of techniques germane to this development by considering a few specific problems.
Abstract: Wereview the current status of multi-dimensional filters bank and wavelet design from the perspective of signal and system theory. The study of wavelets and perfect reconstruction filter banks are known to have roots in traditional filter design techniques. On the other hand, the field of multi-dimensional systems and signal processing has developed a set of tools intrinsic to itself, and has attained a certain level of maturity over the last two decades. We have recently noted a degree of synergy between the two fields of wavelets and multi-dimensional systems. This arises from the fact that many ideas crucial to wavelet design are inherently system theoretic in nature. While there are many examples of this synergy manifested in recent publications, we provide a flavor of techniques germane to this development by considering a few specific problems in detail. The construction of orthogonal wavelets can be essentially viewed as a circuit and system theoretic problem of design of energy dissipative (passive) filters, the multi-dimensional version of which has very close ties with a classic problem of lumped distributed passive network synthesis. Groebner basis techniques, matrix completion problems over rings of polynomials or rings of stable rational functions, i.e., Quillen Suslin (31) type problems are still other examples, which feature in our discussion in an important manner. A number of open problems are also cited. ©1998 The Franklin Institute. Published by Elsevier Science Ltd.

30 citations


Cited by
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Journal ArticleDOI
TL;DR: An algorithm based on Gröbner bases for computing complete systems of solutions (“syzygies”) for linear diophantine equations with multivariate polynomial coefficients is described, showing how many fundamental problems of systems theory can be reduced to the problem of syzyGies computation.
Abstract: We present the basic concepts and results of Grobner bases theory for readers working or interested in systems theory. The concepts and methods of Grobner bases theory are presented by examples. No prerequisites, except some notions of elementary mathematics, are necessary for reading this paper. The two main properties of Grobner bases, the elimination property and the linear independence property, are explained. Most of the many applications of Grobner bases theory, in particular applications in systems theory, hinge on these two properties. Also, an algorithm based on Grobner bases for computing complete systems of solutions (“syzygies”) for linear diophantine equations with multivariate polynomial coefficients is described. Many fundamental problems of systems theory can be reduced to the problem of syzygies computation.

76 citations

Journal ArticleDOI
TL;DR: In this paper, a multivariate polynomial matrix factorization algorithm for computing a globally minimal generating matrix of the syzygy of solutions associated with a Polynomial Matrix Factorization (PMF) is presented.
Abstract: A multivariate polynomial matrix factorization algorithm is introduced and discussed. This algorithm and another algorithm for computing a globally minimal generating matrix of the syzygy of solutions associated with a polynomial matrix are both associated with a zero-coprimeness constraint that characterizes perfect-reconstruction filter banks. Generalizations, as well as limitations of recent results which incorporate the perfect reconstruction as well as the linear-phase constraints, are discussed with several examples and counterexamples. Specifically, a Grobner basis-based proof for perfect reconstruction with linear phase is given for the case of two-band multidimensional filter banks, and the algorithm is illustrated by a nontrivial design example. Progress and bottlenecks in the multidimensional multiband case are also reported.

72 citations

Journal ArticleDOI
TL;DR: A reasonably detailed review is given of several fundamental theoretical issues that occur in the use of Grobner bases in multidimensional signals and systems applications, including the primeness of multivariate polynomial matrices, multivariate unimodularPolynomial matrix completion, and prime factorization of multidity matrices.
Abstract: This paper is a tutorial on Grobner bases and a survey on the applications of Grobner bases in the broad field of signals and systems. A reasonably detailed review is given of several fundamental theoretical issues that occur in the use of Grobner bases in multidimensional signals and systems applications. These topics include the primeness of multivariate polynomial matrices, multivariate unimodular polynomial matrix completion, and prime factorization of multivariate polynomial matrices. A brief review is also presented on the wide-ranging applications of Grobner bases in multidimensional as well as one-dimensional circuits, networks, control, coding, signals, and systems and other related areas like robotics and applied mechanics. The impact and scope of Grobner bases in signals and systems are highlighted with respect to what has already been accomplished as a stepping stone to expanding future research.

60 citations

Journal ArticleDOI
TL;DR: The method casts the design problem as a linear minimization of filter coefficients such that their value at ω = π /2 M is 0.707, which results in a simpler, more direct design procedure.
Abstract: This paper presents a simple and efficient design method for cosine-modulated filter banks with prescribed stopband attenuation, passband ripple, and channel overlap The method casts the design problem as a linear minimization of filter coefficients such that their value at ω = π /2 M is 0707, which results in a simpler, more direct design procedure The weighted constrained least squares technique is exploited for designing the prototype filter for cosine modulation (CM) filter banks Several design examples are included to show the increased efficiency and flexibility of the proposed method over the exiting methods An application of the proposed method is considered in the area of sub-band coding of the ECG and speech signals

44 citations

Journal ArticleDOI
TL;DR: An eigen filter-based approach for the design of two-channel linear-phase FIR perfect-reconstruction (PR) filter banks and shows that, by an appropriate choice of the length of the filters, it can ensure the existence of a solution to the constrained eigenfilter design problem for the complementary-synthesis filter.
Abstract: We present an eigenfilter-based approach for the design of two-channel linear-phase FIR perfect-reconstruction (PR) filter banks. This approach can be used to design 1-D two-channel filter banks, as well as multidimensional nonseparable two-channel filter banks. Our method consists of first designing the low-pass analysis filter. Given the low-pass analysis filter, the PR conditions can be expressed as a set of linear constraints on the complementary-synthesis low-pass filter. We design the complementary-synthesis filter by using the eigenfilter design method with linear constraints. We show that, by an appropriate choice of the length of the filters, we can ensure the existence of a solution to the constrained eigenfilter design problem for the complementary-synthesis filter. Thus, our approach gives an eigenfilter-based method of designing the complementary filter, given a ldquopredesignedrdquo analysis filter, with the filter lengths satisfying certain conditions. We present several design examples to demonstrate the effectiveness of the method.

31 citations