Band Limited Functions and Extensions of Classical Interpolation Series
Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropria...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Madyeh, W. R. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2003 |
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| Schlagwörter: |
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| Anmerkung: |
© SIP 2003 |
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| Übergeordnetes Werk: |
Enthalten in: Sampling theory, signal processing, and data analysis - [Cham] : Birkhäuser, 2021, 2(2003), 2 vom: 01. Mai, Seite 165-189 |
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| Übergeordnetes Werk: |
volume:2 ; year:2003 ; number:2 ; day:01 ; month:05 ; pages:165-189 |
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| DOI / URN: |
10.1007/BF03549392 |
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| 520 | |a Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropriately chosen sampling nodes {xn} = {…,}x0, x1, …. The various specific reconstruction procedures and formulas require additional restrictions on the signal F and the sampling nodes {xn}. Motivated by an article by G. H. Hardy we show, among other things, that every signal F whose frequency band is known can be reconstructed via formulas that are analogous to that provided by the classical Whittaker-Kotelnikov-Shannon Sampling Theorem for signals with finite power. The caveat is that additional samples are required or samples may be deleted depending on the roughness or smoothness of the frequency distribution of F. Viewed from a different perspective, these formulas give rise to relatively natural band limited reconstructions that interpolate the data in cases of finite over or under sampling with respect to the classical sampling theorem. | ||
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10.1007/BF03549392 doi (DE-627)SPR043387276 (SPR)BF03549392-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Madyeh, W. R. verfasserin aut Band Limited Functions and Extensions of Classical Interpolation Series 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropriately chosen sampling nodes {xn} = {…,}x0, x1, …. The various specific reconstruction procedures and formulas require additional restrictions on the signal F and the sampling nodes {xn}. Motivated by an article by G. H. Hardy we show, among other things, that every signal F whose frequency band is known can be reconstructed via formulas that are analogous to that provided by the classical Whittaker-Kotelnikov-Shannon Sampling Theorem for signals with finite power. The caveat is that additional samples are required or samples may be deleted depending on the roughness or smoothness of the frequency distribution of F. Viewed from a different perspective, these formulas give rise to relatively natural band limited reconstructions that interpolate the data in cases of finite over or under sampling with respect to the classical sampling theorem. band limited functions (dpeaa)DE-He213 cardinal series (dpeaa)DE-He213 entire functions of exponential type (dpeaa)DE-He213 Paley-Wiener spaces (dpeaa)DE-He213 sampling theorem (dpeaa)DE-He213 Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 165-189 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:165-189 https://dx.doi.org/10.1007/BF03549392 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 165-189 |
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10.1007/BF03549392 doi (DE-627)SPR043387276 (SPR)BF03549392-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Madyeh, W. R. verfasserin aut Band Limited Functions and Extensions of Classical Interpolation Series 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropriately chosen sampling nodes {xn} = {…,}x0, x1, …. The various specific reconstruction procedures and formulas require additional restrictions on the signal F and the sampling nodes {xn}. Motivated by an article by G. H. Hardy we show, among other things, that every signal F whose frequency band is known can be reconstructed via formulas that are analogous to that provided by the classical Whittaker-Kotelnikov-Shannon Sampling Theorem for signals with finite power. The caveat is that additional samples are required or samples may be deleted depending on the roughness or smoothness of the frequency distribution of F. Viewed from a different perspective, these formulas give rise to relatively natural band limited reconstructions that interpolate the data in cases of finite over or under sampling with respect to the classical sampling theorem. band limited functions (dpeaa)DE-He213 cardinal series (dpeaa)DE-He213 entire functions of exponential type (dpeaa)DE-He213 Paley-Wiener spaces (dpeaa)DE-He213 sampling theorem (dpeaa)DE-He213 Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 165-189 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:165-189 https://dx.doi.org/10.1007/BF03549392 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 165-189 |
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10.1007/BF03549392 doi (DE-627)SPR043387276 (SPR)BF03549392-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Madyeh, W. R. verfasserin aut Band Limited Functions and Extensions of Classical Interpolation Series 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropriately chosen sampling nodes {xn} = {…,}x0, x1, …. The various specific reconstruction procedures and formulas require additional restrictions on the signal F and the sampling nodes {xn}. Motivated by an article by G. H. Hardy we show, among other things, that every signal F whose frequency band is known can be reconstructed via formulas that are analogous to that provided by the classical Whittaker-Kotelnikov-Shannon Sampling Theorem for signals with finite power. The caveat is that additional samples are required or samples may be deleted depending on the roughness or smoothness of the frequency distribution of F. Viewed from a different perspective, these formulas give rise to relatively natural band limited reconstructions that interpolate the data in cases of finite over or under sampling with respect to the classical sampling theorem. band limited functions (dpeaa)DE-He213 cardinal series (dpeaa)DE-He213 entire functions of exponential type (dpeaa)DE-He213 Paley-Wiener spaces (dpeaa)DE-He213 sampling theorem (dpeaa)DE-He213 Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 165-189 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:165-189 https://dx.doi.org/10.1007/BF03549392 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 165-189 |
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10.1007/BF03549392 doi (DE-627)SPR043387276 (SPR)BF03549392-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Madyeh, W. R. verfasserin aut Band Limited Functions and Extensions of Classical Interpolation Series 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropriately chosen sampling nodes {xn} = {…,}x0, x1, …. The various specific reconstruction procedures and formulas require additional restrictions on the signal F and the sampling nodes {xn}. Motivated by an article by G. H. Hardy we show, among other things, that every signal F whose frequency band is known can be reconstructed via formulas that are analogous to that provided by the classical Whittaker-Kotelnikov-Shannon Sampling Theorem for signals with finite power. The caveat is that additional samples are required or samples may be deleted depending on the roughness or smoothness of the frequency distribution of F. Viewed from a different perspective, these formulas give rise to relatively natural band limited reconstructions that interpolate the data in cases of finite over or under sampling with respect to the classical sampling theorem. band limited functions (dpeaa)DE-He213 cardinal series (dpeaa)DE-He213 entire functions of exponential type (dpeaa)DE-He213 Paley-Wiener spaces (dpeaa)DE-He213 sampling theorem (dpeaa)DE-He213 Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 165-189 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:165-189 https://dx.doi.org/10.1007/BF03549392 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 165-189 |
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Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropriately chosen sampling nodes {xn} = {…,}x0, x1, …. The various specific reconstruction procedures and formulas require additional restrictions on the signal F and the sampling nodes {xn}. Motivated by an article by G. H. Hardy we show, among other things, that every signal F whose frequency band is known can be reconstructed via formulas that are analogous to that provided by the classical Whittaker-Kotelnikov-Shannon Sampling Theorem for signals with finite power. The caveat is that additional samples are required or samples may be deleted depending on the roughness or smoothness of the frequency distribution of F. Viewed from a different perspective, these formulas give rise to relatively natural band limited reconstructions that interpolate the data in cases of finite over or under sampling with respect to the classical sampling theorem. © SIP 2003 |
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Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropriately chosen sampling nodes {xn} = {…,}x0, x1, …. The various specific reconstruction procedures and formulas require additional restrictions on the signal F and the sampling nodes {xn}. Motivated by an article by G. H. Hardy we show, among other things, that every signal F whose frequency band is known can be reconstructed via formulas that are analogous to that provided by the classical Whittaker-Kotelnikov-Shannon Sampling Theorem for signals with finite power. The caveat is that additional samples are required or samples may be deleted depending on the roughness or smoothness of the frequency distribution of F. Viewed from a different perspective, these formulas give rise to relatively natural band limited reconstructions that interpolate the data in cases of finite over or under sampling with respect to the classical sampling theorem. © SIP 2003 |
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Abstract Many of the algorithms and results generated by the mathematics of signal processing and its associated sampling theory rely on the fact that every signal F(x), −∞ < x < ∞, which is frequency band limited, can be reconstructed from a discrete sequence of samples {F(xn)} with appropriately chosen sampling nodes {xn} = {…,}x0, x1, …. The various specific reconstruction procedures and formulas require additional restrictions on the signal F and the sampling nodes {xn}. Motivated by an article by G. H. Hardy we show, among other things, that every signal F whose frequency band is known can be reconstructed via formulas that are analogous to that provided by the classical Whittaker-Kotelnikov-Shannon Sampling Theorem for signals with finite power. The caveat is that additional samples are required or samples may be deleted depending on the roughness or smoothness of the frequency distribution of F. Viewed from a different perspective, these formulas give rise to relatively natural band limited reconstructions that interpolate the data in cases of finite over or under sampling with respect to the classical sampling theorem. © SIP 2003 |
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Band Limited Functions and Extensions of Classical Interpolation Series |
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