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Proceedings Paper

Image Processing and the Arithmetic Fourier Trans-form
Author(s): D W Tufts; Z Fan; Z Cao
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Paper Abstract

A new Fourier technique, the Arithmetic Fourier Transform (AFT) was recently developed for signal processing. This approach is based on the number-theoretic method of Mobius inversion. The AFT needs only additions except for a small amount of multiplications by prescribed scale factors. This new algorithm is also well suited to parallel processing. And there is no accumulation of rounding errors in the AFT algorithm. In this paper, the AFT is used to compute the discrete cosine transform and is also extended to 2-D cases for image processing. A 2-D Mobius inversion formula is proved. It is then applied to the computation of Fourier coefficients of a periodic 2-D function. It is shown that the output of an array of delay-line (or transversal) filters is the Mobius transform of the input harmonic terms. The 2-D Fourier coefficients can therefore be obtained through Mobius inversion of the output the filter array.

Paper Details

Date Published: 17 May 1989
PDF: 8 pages
Proc. SPIE 1058, High Speed Computing II, (17 May 1989); doi: 10.1117/12.951665
Show Author Affiliations
D W Tufts, University of Rhode Island (United States)
Z Fan, University of Rhode Island (United States)
Z Cao, University of Rhode Island (United States)

Published in SPIE Proceedings Vol. 1058:
High Speed Computing II
Keith Bromley, Editor(s)

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