Convolution theorems: partitioning the space of integral transforms

Alan R. Lindsey; Bruce W. Suter

doi:10.1117/12.342937

22 March 1999 Convolution theorems: partitioning the space of integral transforms

Alan R. Lindsey, Bruce W. Suter

Proceedings Volume 3723, Wavelet Applications VI; (1999) https://doi.org/10.1117/12.342937
Event: AeroSense '99, 1999, Orlando, FL, United States

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.

Citation Download Citation

Alan R. Lindsey and Bruce W. Suter "Convolution theorems: partitioning the space of integral transforms", Proc. SPIE 3723, Wavelet Applications VI, (22 March 1999); https://doi.org/10.1117/12.342937

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