Fast Fourier Transform for Hexagonal Aggregates |
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Authors: | Jaime L Zapata Gerhard X Ritter |
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Affiliation: | (1) Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA;(2) Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA |
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Abstract: | Hexagonal aggregates are hierarchical arrangements of hexagonal cells. These hexagonal cells may be efficiently addressed using a scheme known as generalized balanced ternary for dimension 2, or GBT2. The objects of interest in this paper are digital images whose domains are hexagonal aggregates. We define a discrete Fourier transform (DFT) for such images. The main result of this paper is a radix-7, decimation-in-space fast Fourier transform (FFT) for images defined on hexagonal aggregates. The algorithm has complexity N log7 N. It is expressed in terms of the p-product, a generalization of matrix multiplication. Data reordering (also known as shuffle permutations) is generally associated with FFT algorithms. However, use of the p-product makes data reordering unnecessary. |
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Keywords: | hexagonal aggregates fast Fourier transforms generalized balanced ternary p-product algorithm |
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