Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform

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 coordi...
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Autor*in:	Xueyang Yao [verfasserIn] Natalie Baddour [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Fourier theory DFT in polar coordinates Polar coordinates Multidimensional DFT Discrete Hankel Transform Discrete Fourier Transform

Übergeordnetes Werk:	In: PeerJ Computer Science - PeerJ Inc., 2016, 6, p e257(2020)
Übergeordnetes Werk:	volume:6, p e257 ; year:2020

Links:	Link aufrufen Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.7717/peerj-cs.257

Katalog-ID:	DOAJ037992384

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520			\|a 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 and inverse DFT sequence can be exploited for coding. 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.
650		4	\|a Fourier theory
650		4	\|a DFT in polar coordinates
650		4	\|a Polar coordinates
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650		4	\|a Discrete Hankel Transform
650		4	\|a Discrete Fourier Transform
653		0	\|a Electronic computers. Computer science
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allfieldsGer	10.7717/peerj-cs.257 doi (DE-627)DOAJ037992384 (DE-599)DOAJ88cf45f31cc44d2d93c78639fb953cd4 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Xueyang Yao verfasserin aut Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 and inverse DFT sequence can be exploited for coding. 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. Fourier theory DFT in polar coordinates Polar coordinates Multidimensional DFT Discrete Hankel Transform Discrete Fourier Transform Electronic computers. Computer science Natalie Baddour verfasserin aut In PeerJ Computer Science PeerJ Inc., 2016 6, p e257(2020) (DE-627)867969210 (DE-600)2868384-5 23765992 nnns volume:6, p e257 year:2020 https://doi.org/10.7717/peerj-cs.257 kostenfrei https://doaj.org/article/88cf45f31cc44d2d93c78639fb953cd4 kostenfrei https://peerj.com/articles/cs-257.pdf kostenfrei https://peerj.com/articles/cs-257/ kostenfrei https://doaj.org/toc/2376-5992 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6, p e257 2020
allfieldsSound	10.7717/peerj-cs.257 doi (DE-627)DOAJ037992384 (DE-599)DOAJ88cf45f31cc44d2d93c78639fb953cd4 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Xueyang Yao verfasserin aut Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 and inverse DFT sequence can be exploited for coding. 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. Fourier theory DFT in polar coordinates Polar coordinates Multidimensional DFT Discrete Hankel Transform Discrete Fourier Transform Electronic computers. Computer science Natalie Baddour verfasserin aut In PeerJ Computer Science PeerJ Inc., 2016 6, p e257(2020) (DE-627)867969210 (DE-600)2868384-5 23765992 nnns volume:6, p e257 year:2020 https://doi.org/10.7717/peerj-cs.257 kostenfrei https://doaj.org/article/88cf45f31cc44d2d93c78639fb953cd4 kostenfrei https://peerj.com/articles/cs-257.pdf kostenfrei https://peerj.com/articles/cs-257/ kostenfrei https://doaj.org/toc/2376-5992 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6, p e257 2020
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author	Xueyang Yao
spellingShingle	Xueyang Yao misc QA75.5-76.95 misc Fourier theory misc DFT in polar coordinates misc Polar coordinates misc Multidimensional DFT misc Discrete Hankel Transform misc Discrete Fourier Transform misc Electronic computers. Computer science Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform
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topic_title	QA75.5-76.95 Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform Fourier theory DFT in polar coordinates Polar coordinates Multidimensional DFT Discrete Hankel Transform Discrete Fourier Transform
topic	misc QA75.5-76.95 misc Fourier theory misc DFT in polar coordinates misc Polar coordinates misc Multidimensional DFT misc Discrete Hankel Transform misc Discrete Fourier Transform misc Electronic computers. Computer science
topic_unstemmed	misc QA75.5-76.95 misc Fourier theory misc DFT in polar coordinates misc Polar coordinates misc Multidimensional DFT misc Discrete Hankel Transform misc Discrete Fourier Transform misc Electronic computers. Computer science
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title	Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform
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title_auth	Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform
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 and inverse DFT sequence can be exploited for coding. 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.
abstractGer	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 and inverse DFT sequence can be exploited for coding. 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.
abstract_unstemmed	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 and inverse DFT sequence can be exploited for coding. 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.
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title_short	Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform
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Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform

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