A Framework for Discrete Integral Transformations I-The Pseudopolar Fourier Transform (original) (raw)

Computing the Fourier transform of a function in polar coordinates is an important building block in many scientific disciplines and numerical schemes. In this paper we present the pseudo-polar Fourier transform that samples the Fourier transform on the pseudo-polar grid, also know as the concentric squares grid. The pseudo-polar grid consists of equally spaced samples along rays, where different rays are equally spaced and not equally angled. The pseudo-polar Fourier transform Fourier transform is shown to be fast (the same complexity as the FFT), stable, invertible, requires only 1D operations, and uses no interpolations. We prove that the pseudo-polar Fourier transform is invertible and develop two algorithms for its inversion: