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Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

Dovlo E, Baddour N - MethodsX (2015)

Bottom Line: The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented.By examining a function in the frequency domain, additional information and insights may be obtained.The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

View Article: PubMed Central - PubMed

Affiliation: Centre for Advanced Diffusion-Wave Technologies (CADIFT), Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Rd., Toronto, ON M5S 3G8, Canada.

ABSTRACT
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

No MeSH data available.


Plot of the (a)  and its 2D polar Fourier transform, (b) .
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fig0005: Plot of the (a) and its 2D polar Fourier transform, (b) .

Mentions: The direct method produces an indeterminate result whereas the indirect method gives a definite and accurate result. The plots of the shifted Dirac-delta expression and its transform are provided in Fig. 1.


Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

Dovlo E, Baddour N - MethodsX (2015)

Plot of the (a)  and its 2D polar Fourier transform, (b) .
© Copyright Policy - CC BY
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4487714&req=5

fig0005: Plot of the (a) and its 2D polar Fourier transform, (b) .
Mentions: The direct method produces an indeterminate result whereas the indirect method gives a definite and accurate result. The plots of the shifted Dirac-delta expression and its transform are provided in Fig. 1.

Bottom Line: The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented.By examining a function in the frequency domain, additional information and insights may be obtained.The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

View Article: PubMed Central - PubMed

Affiliation: Centre for Advanced Diffusion-Wave Technologies (CADIFT), Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Rd., Toronto, ON M5S 3G8, Canada.

ABSTRACT
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

No MeSH data available.