Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform

Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear tra...
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Autor*in:	Serbes, Ahmet [verfasserIn] Durak-Ata (EURASIP Member), Lutfiye [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2010

Schlagwörter:	Discrete Fourier Transform Eigenvalue Decomposition Taylor Approximation Chirp Rate Analog Domain

Übergeordnetes Werk:	Enthalten in: EURASIP journal on advances in signal processing - Heidelberg : Springer, 2007, 2010(2010), 1 vom: 14. Juli
Übergeordnetes Werk:	volume:2010 ; year:2010 ; number:1 ; day:14 ; month:07

Links:	Volltext

DOI / URN:	10.1155/2010/191085

Katalog-ID:	SPR03199315X

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520			\|a Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As j in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain, it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations.
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spelling	10.1155/2010/191085 doi (DE-627)SPR03199315X (SPR)191085-e DE-627 ger DE-627 rakwb eng 620 ASE 53.73 bkl Serbes, Ahmet verfasserin aut Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As j in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain, it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations. Discrete Fourier Transform (dpeaa)DE-He213 Eigenvalue Decomposition (dpeaa)DE-He213 Taylor Approximation (dpeaa)DE-He213 Chirp Rate (dpeaa)DE-He213 Analog Domain (dpeaa)DE-He213 Durak-Ata (EURASIP Member), Lutfiye verfasserin aut Enthalten in EURASIP journal on advances in signal processing Heidelberg : Springer, 2007 2010(2010), 1 vom: 14. Juli (DE-627)534054277 (DE-600)2364203-8 1687-6180 nnns volume:2010 year:2010 number:1 day:14 month:07 https://dx.doi.org/10.1155/2010/191085 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_2014 GBV_ILN_2522 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 53.73 ASE AR 2010 2010 1 14 07
allfields_unstemmed	10.1155/2010/191085 doi (DE-627)SPR03199315X (SPR)191085-e DE-627 ger DE-627 rakwb eng 620 ASE 53.73 bkl Serbes, Ahmet verfasserin aut Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As j in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain, it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations. Discrete Fourier Transform (dpeaa)DE-He213 Eigenvalue Decomposition (dpeaa)DE-He213 Taylor Approximation (dpeaa)DE-He213 Chirp Rate (dpeaa)DE-He213 Analog Domain (dpeaa)DE-He213 Durak-Ata (EURASIP Member), Lutfiye verfasserin aut Enthalten in EURASIP journal on advances in signal processing Heidelberg : Springer, 2007 2010(2010), 1 vom: 14. Juli (DE-627)534054277 (DE-600)2364203-8 1687-6180 nnns volume:2010 year:2010 number:1 day:14 month:07 https://dx.doi.org/10.1155/2010/191085 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_2014 GBV_ILN_2522 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 53.73 ASE AR 2010 2010 1 14 07
allfieldsGer	10.1155/2010/191085 doi (DE-627)SPR03199315X (SPR)191085-e DE-627 ger DE-627 rakwb eng 620 ASE 53.73 bkl Serbes, Ahmet verfasserin aut Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As j in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain, it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations. Discrete Fourier Transform (dpeaa)DE-He213 Eigenvalue Decomposition (dpeaa)DE-He213 Taylor Approximation (dpeaa)DE-He213 Chirp Rate (dpeaa)DE-He213 Analog Domain (dpeaa)DE-He213 Durak-Ata (EURASIP Member), Lutfiye verfasserin aut Enthalten in EURASIP journal on advances in signal processing Heidelberg : Springer, 2007 2010(2010), 1 vom: 14. Juli (DE-627)534054277 (DE-600)2364203-8 1687-6180 nnns volume:2010 year:2010 number:1 day:14 month:07 https://dx.doi.org/10.1155/2010/191085 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_2014 GBV_ILN_2522 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 53.73 ASE AR 2010 2010 1 14 07
allfieldsSound	10.1155/2010/191085 doi (DE-627)SPR03199315X (SPR)191085-e DE-627 ger DE-627 rakwb eng 620 ASE 53.73 bkl Serbes, Ahmet verfasserin aut Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As j in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain, it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations. Discrete Fourier Transform (dpeaa)DE-He213 Eigenvalue Decomposition (dpeaa)DE-He213 Taylor Approximation (dpeaa)DE-He213 Chirp Rate (dpeaa)DE-He213 Analog Domain (dpeaa)DE-He213 Durak-Ata (EURASIP Member), Lutfiye verfasserin aut Enthalten in EURASIP journal on advances in signal processing Heidelberg : Springer, 2007 2010(2010), 1 vom: 14. Juli (DE-627)534054277 (DE-600)2364203-8 1687-6180 nnns volume:2010 year:2010 number:1 day:14 month:07 https://dx.doi.org/10.1155/2010/191085 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_2014 GBV_ILN_2522 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 53.73 ASE AR 2010 2010 1 14 07
language	English
source	Enthalten in EURASIP journal on advances in signal processing 2010(2010), 1 vom: 14. Juli volume:2010 year:2010 number:1 day:14 month:07
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topic_facet	Discrete Fourier Transform Eigenvalue Decomposition Taylor Approximation Chirp Rate Analog Domain
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author	Serbes, Ahmet
spellingShingle	Serbes, Ahmet ddc 620 bkl 53.73 misc Discrete Fourier Transform misc Eigenvalue Decomposition misc Taylor Approximation misc Chirp Rate misc Analog Domain Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform
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topic_title	620 ASE 53.73 bkl Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform Discrete Fourier Transform (dpeaa)DE-He213 Eigenvalue Decomposition (dpeaa)DE-He213 Taylor Approximation (dpeaa)DE-He213 Chirp Rate (dpeaa)DE-He213 Analog Domain (dpeaa)DE-He213
topic	ddc 620 bkl 53.73 misc Discrete Fourier Transform misc Eigenvalue Decomposition misc Taylor Approximation misc Chirp Rate misc Analog Domain
topic_unstemmed	ddc 620 bkl 53.73 misc Discrete Fourier Transform misc Eigenvalue Decomposition misc Taylor Approximation misc Chirp Rate misc Analog Domain
topic_browse	ddc 620 bkl 53.73 misc Discrete Fourier Transform misc Eigenvalue Decomposition misc Taylor Approximation misc Chirp Rate misc Analog Domain
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title	Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform
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title_full	Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform
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title_sort	eigenvectors of the discrete fourier transform based on the bilinear transform
title_auth	Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform
abstract	Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As j in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain, it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations.
abstractGer	Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As j in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain, it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations.
abstract_unstemmed	Abstract Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As j in the analog s-domain is mapped to the unit circle one-to-one without aliasing in the discrete z-domain, it is appropriate to use it in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT matrix. For this purpose we propose three different methods and analyze their stability conditions. These methods include better conditioned commuting matrices and higher order methods. We confirm the results with extensive simulations.
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title_short	Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform
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