Discrete Two Dimensional Fourier Transform in Polar Coordinates Part II: Numerical Computation and Approximation of the Continuous Transform
| Autor: | Xueyang Yao, Natalie Baddour |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
General Computer Science
Inverse 02 engineering and technology 01 natural sciences lcsh:QA75.5-76.95 Convolution 010309 optics Discrete Fourier transform (general) symbols.namesake Scientific Computing and Simulation Orthogonality 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Physics::Atomic and Molecular Clusters Discrete Fourier Transform Physics::Chemical Physics Physics Hankel transform applied_mathematics Series (mathematics) Mathematical analysis Theory and Formal Methods Fourier theory DFT in polar coordinates 020206 networking & telecommunications Multidimensional DFT Polar coordinates Fourier transform Algorithms and Analysis of Algorithms symbols lcsh:Electronic computers. Computer science Polar coordinate system Discrete Hankel Transform |
| Zdroj: | PeerJ Computer Science, Vol 6, p e257 (2020) PeerJ Computer Science |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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