A fast high accuracy Polar FFT algorithm is given in the software package written in MATLAB. For a given 2D signal of size n×n, the algorihtm s complexity is just like in a Cartesian 2D-FFT, which can be used widely in image processing and analysis.

Polar Fourier Transform\AFTUSF_NGP_1.m
.......................\AFTUSF_Spline_1.m
.......................\APPFFT.m
.......................\A_Content.m
.......................\Bilinear_Interp_Matrix.m
.......................\Brute_Force_Transform.m
.......................\Cartesian_2_Polar.m
.......................\Compare_Bilinear_Interpolations.m
.......................\Comparison_1_USFT_vs_Polar.m
.......................\Comparison_2_USFT_vs_Polar.m
.......................\Comparison_3_USFT_vs_Polar.m
.......................\Comparison_4_Polar_Corner.m
.......................\Create_Figures_For_paper.m
.......................\Create_Grid.m
.......................\Create_Oversampled_Grid.m
.......................\Debug_interp_SPLINE.m
.......................\Debug_XPolar_FFT.m
.......................\Disk_Relative_Energy.m
.......................\Distance_from_Grid.m
.......................\Distinct.m
.......................\Error_Analysis_1.m
.......................\Error_Analysis_2.m
.......................\Error_Analysis_3.m
.......................\Example_Image1.jpg
.......................\Grid_Evolution.m
.......................\interp_SPLINE.m
.......................\IPPFFT.m
.......................\lena.tif
.......................\My_FRFT.m
.......................\My_FRFT_Centered.m
.......................\PFFT.m
.......................\Polar_Transform_New.m
.......................\PPFFT.m
.......................\Pseudo_Polar_Evolution.m
.......................\Ray_Behavior.m
.......................\RectoPolar_Trans_Adjoint.m
.......................\RectoPolar_Trans_New.m
.......................\SPolar_Transform.m
.......................\Test_FRFT.m
.......................\Transform_Matrix.m
.......................\XPolar_Transform.m
Polar Fourier Transform

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