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

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.

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