Journal ArticleDOI
Fourfold rotational symmetry in two-dimensional functions
TLDR
In this paper, the magnitude functions of the frequency responses of two-dimensional analog and digital transfer functions were derived so that the magnitude function of these transfer functions possess fourfold rotational symmetry.Abstract:
The presence of various types of symmetry in the frequency responses of a two-dimensional filter function reflects as constraints on its coefficients. In this paper, such constraints are derived for two-dimensional analog and digital transfer functions so that the magnitude functions of the frequency responses of these transfer functions possess fourfold rotational symmetry. The relationship between fourfold rotational symmetry and quadrantal, diagonal, and octagonal symmetries is also discussed.read more
Citations
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Journal ArticleDOI
2-D symmetry: theory and filter design applications
TL;DR: The theory of symmetry in two-dimensional (2-D) filter functions and in 2-D Fourier transforms is presented and it is shown that when a filter frequency response possesses symmetry, the realization problem becomes relatively simple.
Proceedings ArticleDOI
Multidimensional wave-digital principles: from filtering to numerical integration
TL;DR: Wave-digital principles, originally developed for one-dimensional filtering purposes, have later been extended to multidimensional filtering applications and have been shown to be applicable also to numerical integration of physically relevant ordinary and partial differential equations of linear and nonlinear type.
Journal ArticleDOI
Multidimensional digital filters with closed loss behavior designed by complex network theory approach
TL;DR: A very efficient design approach is presented for designing compact multidimensional digital filters having closed loss behavior (e.g., loss behavior with approximately circular, spherical, etc., symmetry).
Journal ArticleDOI
Symmetry Study for Delta- Operator-Based 2-D Digital Filters
TL;DR: This work comprehensively establishes the theory of constraints for delta-operator formulated discrete-time real-coefficient polynomials and functions, arising out of the many types of symmetries in their magnitude responses, and presents a least square error criterion based procedure to design 2-D digital filters in gamma-domain that utilizes the symmetry properties of the magnitude specification.
Journal ArticleDOI
Coset Sum: An Alternative to the Tensor Product in Wavelet Construction
Youngmi Hur,Fang Zheng +1 more
TL;DR: The coset sum shares many essential features of the tensor product that make it attractive in practice and suggest that it is worthwhile to develop and practice alternative methods to the Tensor product for constructing multivariate wavelet systems.
References
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Journal ArticleDOI
Two-dimensional spectral factorization with applications in recursive digital filtering
M. Ekstrom,John W. Woods +1 more
TL;DR: In this article, the concept of spectral factorization is extended to two dimensions in such a way as to preserve the analytic characteristics of the factors, and the resulting factors are shown to be recursively computable and stable in agreement with one-dimensional (1-D) spectral factorisation.
Journal ArticleDOI
Two-dimensional digital filtering
TL;DR: The problems of designing and implementing LSI systems for the processing of 2-D digital data, such as images or geophone arrays, are reviewed and discussed.
Journal ArticleDOI
Quadrantal symmetry associated with two-dimensional digital transfer functions
P. Karivaratharajan,M. Swamy +1 more
TL;DR: In this article, the class of two-dimensional (2D) digital transfer functions which possess quadrantal symmetry in their frequency responses is derived and application of this class in the design of 2-D recursive digital filters is indicated.
Journal ArticleDOI
Computer-aided design of separable two-dimensional digital filters
R.E. Twogood,Sanjit K. Mitra +1 more
TL;DR: A procedure for the design of separable two-dimensional digital filters is presented and the computation involved in both the filter design and implementation is shown to be efficient.
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