Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple

The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. A toolbox of functions for the computation of two dimensional Fourier transforms in polar coordinates with symbolic computer algebra (Maple) was devel...

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Main Authors: Edem Dovlo, Natalie Baddour
Format: Article
Language:English
Published: Ubiquity Press 2015-02-01
Series:Journal of Open Research Software
Subjects:
Online Access:http://openresearchsoftware.metajnl.com/articles/52
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author Edem Dovlo
Natalie Baddour
author_facet Edem Dovlo
Natalie Baddour
author_sort Edem Dovlo
collection DOAJ
description The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. A toolbox of functions for the computation of two dimensional Fourier transforms in polar coordinates with symbolic computer algebra (Maple) was developed. The implementation of the 2D Fourier transform in polar coordinates within the toolbox is a combination of two significantly simpler transforms. A modular approach is used along with the idea of lookup tables to help avoid the issue of indeterminate results when attempting to directly evaluate the transform. This concept helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.
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spelling doaj.art-9db18a1edfed4961b882e4c5d5e546962022-12-22T01:14:01ZengUbiquity PressJournal of Open Research Software2049-96472015-02-0131e3e310.5334/jors.bo48Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via MapleEdem Dovlo0Natalie Baddour1University of TorontoUniversity of OttawaThe Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. A toolbox of functions for the computation of two dimensional Fourier transforms in polar coordinates with symbolic computer algebra (Maple) was developed. The implementation of the 2D Fourier transform in polar coordinates within the toolbox is a combination of two significantly simpler transforms. A modular approach is used along with the idea of lookup tables to help avoid the issue of indeterminate results when attempting to directly evaluate the transform. This concept helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.http://openresearchsoftware.metajnl.com/articles/52Fourier Transforms, Hankel Transforms, Multidimensional Transforms, Polar Coordinates
spellingShingle Edem Dovlo
Natalie Baddour
Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple
Journal of Open Research Software
Fourier Transforms, Hankel Transforms, Multidimensional Transforms, Polar Coordinates
title Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple
title_full Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple
title_fullStr Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple
title_full_unstemmed Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple
title_short Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple
title_sort toolbox for the computation of 2d fourier transforms in polar coordinates via maple
topic Fourier Transforms, Hankel Transforms, Multidimensional Transforms, Polar Coordinates
url http://openresearchsoftware.metajnl.com/articles/52
work_keys_str_mv AT edemdovlo toolboxforthecomputationof2dfouriertransformsinpolarcoordinatesviamaple
AT nataliebaddour toolboxforthecomputationof2dfouriertransformsinpolarcoordinatesviamaple