NDLI: Algebraic Signal Processing Theory: 2-D Spatial Hexagonal Lattice

Content Provider	IEEE Xplore Digital Library
Author	Puschel, M. Rotteler, M.
Copyright Year	1992
Abstract	We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper
Sponsorship	IEEE Signal Processing Society
Page Count	16
File Size	1449116
Starting Page	1506
Ending Page	1521
File Format	PDF
ISSN	10577149
Volume Number	16
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Signal processing Lattices Fourier transforms Array signal processing Discrete Fourier transforms Boundary conditions Filtering Convolution Frequency response Discrete transforms spectrum Chebyshev polynomials in two variables convolution discrete cosine transform (DCT) discrete triangle transform (DTT) nonseparable polynomial algebra representation theory
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

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