Yao X, Baddour N. 2020. Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform. PeerJ Computer Science 6:e257 https://doi.org/10.7717/peerj-cs.257
Yao X, Baddour N. 2020. Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform. PeerJ Computer Science 6:e257 https://doi.org/10.7717/peerj-cs.257
Yao X, Baddour N. 2020. Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform. PeerJ Computer Science 6:e257 https://doi.org/10.7717/peerj-cs.257
Yao X, Baddour N. 2020. Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform. PeerJ Computer Science 6:e257 https://doi.org/10.7717/peerj-cs.257
Abstract
The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
