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Proceedings Paper

Diagonal forms of symmetric convolution matrices for asymmetric multidimensional sequences
Author(s): Thomas M. Foltz; Byron M. Welsh
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Paper Abstract

This paper presents diagonal forms of matrices representing symmetric convolution which is the underlying form of convolution for discrete trigonometric transforms. Symmetric convolution is identically equivalent to linear convolution for appropriately zero-padded sequences. These diagonal forms provide an alternate derivation of the symmetric convolution-multiplication property of the discrete trigonometric transforms. Derived in this manner, the symmetric convolution-multiplication property extends easily to multiple dimensions, and generalizes to multidimensional asymmetric sequences. The symmetric convolution of multidimensional asymmetric sequences can then be accomplished by taking the product of the trigonometric transforms of the sequences and then applying an inverse transform to the result. An example is given of how this theory can be used for applying a 2D FIR filter with nonlinear phase which models atmospheric turbulence.

Paper Details

Date Published: 1 October 1998
PDF: 12 pages
Proc. SPIE 3460, Applications of Digital Image Processing XXI, (1 October 1998); doi: 10.1117/12.323174
Show Author Affiliations
Thomas M. Foltz, Air Force Institute of Technology (United States)
Byron M. Welsh, Air Force Institute of Technology (United States)

Published in SPIE Proceedings Vol. 3460:
Applications of Digital Image Processing XXI
Andrew G. Tescher, Editor(s)

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