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Proceedings Paper

Convolution theorems: partitioning the space of integral transforms
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Paper Abstract

Investigating a number of different integral transforms uncovers distinct patterns in the type of translation convolution theorems afforded by each. It is shown that transforms based on separable kernels (aka Fourier, Laplace and their relatives) have a form of the convolution theorem providing for a transform domain product of the convolved functions. However, transforms based on kernels not separable in the function and transform variables mandate a convolution theorem of a different type; namely in the transform domain the convolution becomes another convolution--one function with the transform of the other.

Paper Details

Date Published: 22 March 1999
PDF: 9 pages
Proc. SPIE 3723, Wavelet Applications VI, (22 March 1999); doi: 10.1117/12.342937
Show Author Affiliations
Alan R. Lindsey, Air Force Research Lab. (United States)
Bruce W. Suter, Air Force Research Lab. (United States)

Published in SPIE Proceedings Vol. 3723:
Wavelet Applications VI
Harold H. Szu, Editor(s)

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