Journal ArticleDOI
Sum and product separabilities of multivariable functions and applications
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TLDR
In this article, necessary and sufficient conditions for reducibility of certain classes of multivariable polynomials are considered, and the special case when a polynomial in that class can be factored into a finite product of single variable p.r.Abstract:
Necessary and sufficient conditions for reducibility of certain classes of multivariable polynomials are considered. The special case when a polynomial in that class can be factored into a finite product of single variable polynomials is investigated. A set of necessary and sufficient conditions for decomposing a multivariable p.r.f. into a sum of single variable p.r.f.'s is given. Examples to illustrate applications of sum and product separabilities of functions are given.read more
Citations
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Journal ArticleDOI
The LU decomposition theorem and its implications to the realization of two-dimensional digital filters
TL;DR: It is shown that if a canonical 2-D IIR filter is realizable, then a realizable LU decomposition form can be always obtained, a property that is not shared by the JD and SV decomposition forms.
Journal ArticleDOI
A decomposition theorem and its implications to the design and realization of two-dimensional filters
TL;DR: It is shown that an arbitrary rational 2-D transfer function can be expanded in first order terms, each one of which is a function of only one of the two variables.
Journal ArticleDOI
Problems and progress in multidimensional systems theory
TL;DR: The troubles and trends of research in multidimensional system theory are presented, with special emphasis in the areas of multivariable network analysis and synthesis, and multiddimensional digital filters.
Journal ArticleDOI
Stabilization of certain two-dimensional recursive digital filters
TL;DR: In this article, a stabilization technique for one-dimensional recursive digital filters was proposed via a conjecture, which states that the planar least squares inverse of a two-dimensional filter polynomial is minimum phase and hence stable.
Journal ArticleDOI
Analysis and synthesis of a class of nonlinear systems
K. Shanmugam,M. Lal +1 more
TL;DR: In this paper, a unified approach for the analysis and synthesis of a class of nonlinear systems is discussed, based on the Volterra series representation of the input/output relationship.
References
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Image processing
TL;DR: Parts of image processing are discussed--specifically: the mathematical operations one is likely to encounter, and ways of implementing them by optics and on digital computers; image description; and image quality evaluation.
Journal ArticleDOI
Stability and synthesis of two-dimensional recursive filters
J. Shanks,S. Treitel,J. Justice +2 more
TL;DR: Two-dimensional recursive bandpass filters as mentioned in this paper can be synthesized to approximate large varieties of desired two-dimensional pulse responses by a conformal transformation of the one-dimensional filters.
Journal ArticleDOI
Synthesis of Finite Passive n-Ports with Prescribed Positive Real Matrices of Several Variables
TL;DR: In this paper, a general solution to the problem of synthesizing positive real functions and matrices of several variables has been presented, except for the two-variable lossless case and the case where a twovariable positive real function is prescribed as a bilinear function with respect to one of the two variables.
Journal ArticleDOI
A criterion to determine if two multivariable polynomials are relatively prime
TL;DR: In this article, a necessary and sufficient condition to determine whether any two multivariable polynomials are relatively prime or not is given, and two simple examples are included to illustrate the applicability of the foregoing condition.