Uncertainty Inequalities for the Linear Canonical Hilbert Transform
Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequa...
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Xu, Shuiqing [verfasserIn] |
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Artikel |
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Englisch |
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2018 |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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| Übergeordnetes Werk: |
Enthalten in: Circuits, systems and signal processing - Springer US, 1982, 37(2018), 10 vom: 07. März, Seite 4584-4598 |
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volume:37 ; year:2018 ; number:10 ; day:07 ; month:03 ; pages:4584-4598 |
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10.1007/s00034-018-0780-1 |
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| 520 | |a Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. | ||
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10.1007/s00034-018-0780-1 doi (DE-627)OLC2034852885 (DE-He213)s00034-018-0780-1-p DE-627 ger DE-627 rakwb eng 600 VZ Xu, Shuiqing verfasserin aut Uncertainty Inequalities for the Linear Canonical Hilbert Transform 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. Uncertainty inequalities Linear canonical Hilbert transform Linear canonical transform Chai, Yi aut Hu, Youqiang aut Feng, Li aut Huang, Lei aut Enthalten in Circuits, systems and signal processing Springer US, 1982 37(2018), 10 vom: 07. März, Seite 4584-4598 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:37 year:2018 number:10 day:07 month:03 pages:4584-4598 https://doi.org/10.1007/s00034-018-0780-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_70 GBV_ILN_2244 AR 37 2018 10 07 03 4584-4598 |
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10.1007/s00034-018-0780-1 doi (DE-627)OLC2034852885 (DE-He213)s00034-018-0780-1-p DE-627 ger DE-627 rakwb eng 600 VZ Xu, Shuiqing verfasserin aut Uncertainty Inequalities for the Linear Canonical Hilbert Transform 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. Uncertainty inequalities Linear canonical Hilbert transform Linear canonical transform Chai, Yi aut Hu, Youqiang aut Feng, Li aut Huang, Lei aut Enthalten in Circuits, systems and signal processing Springer US, 1982 37(2018), 10 vom: 07. März, Seite 4584-4598 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:37 year:2018 number:10 day:07 month:03 pages:4584-4598 https://doi.org/10.1007/s00034-018-0780-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_70 GBV_ILN_2244 AR 37 2018 10 07 03 4584-4598 |
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10.1007/s00034-018-0780-1 doi (DE-627)OLC2034852885 (DE-He213)s00034-018-0780-1-p DE-627 ger DE-627 rakwb eng 600 VZ Xu, Shuiqing verfasserin aut Uncertainty Inequalities for the Linear Canonical Hilbert Transform 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. Uncertainty inequalities Linear canonical Hilbert transform Linear canonical transform Chai, Yi aut Hu, Youqiang aut Feng, Li aut Huang, Lei aut Enthalten in Circuits, systems and signal processing Springer US, 1982 37(2018), 10 vom: 07. März, Seite 4584-4598 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:37 year:2018 number:10 day:07 month:03 pages:4584-4598 https://doi.org/10.1007/s00034-018-0780-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_70 GBV_ILN_2244 AR 37 2018 10 07 03 4584-4598 |
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10.1007/s00034-018-0780-1 doi (DE-627)OLC2034852885 (DE-He213)s00034-018-0780-1-p DE-627 ger DE-627 rakwb eng 600 VZ Xu, Shuiqing verfasserin aut Uncertainty Inequalities for the Linear Canonical Hilbert Transform 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. Uncertainty inequalities Linear canonical Hilbert transform Linear canonical transform Chai, Yi aut Hu, Youqiang aut Feng, Li aut Huang, Lei aut Enthalten in Circuits, systems and signal processing Springer US, 1982 37(2018), 10 vom: 07. März, Seite 4584-4598 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:37 year:2018 number:10 day:07 month:03 pages:4584-4598 https://doi.org/10.1007/s00034-018-0780-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_70 GBV_ILN_2244 AR 37 2018 10 07 03 4584-4598 |
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10.1007/s00034-018-0780-1 doi (DE-627)OLC2034852885 (DE-He213)s00034-018-0780-1-p DE-627 ger DE-627 rakwb eng 600 VZ Xu, Shuiqing verfasserin aut Uncertainty Inequalities for the Linear Canonical Hilbert Transform 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. Uncertainty inequalities Linear canonical Hilbert transform Linear canonical transform Chai, Yi aut Hu, Youqiang aut Feng, Li aut Huang, Lei aut Enthalten in Circuits, systems and signal processing Springer US, 1982 37(2018), 10 vom: 07. März, Seite 4584-4598 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:37 year:2018 number:10 day:07 month:03 pages:4584-4598 https://doi.org/10.1007/s00034-018-0780-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_70 GBV_ILN_2244 AR 37 2018 10 07 03 4584-4598 |
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Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2034852885</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230331224851.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2018 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00034-018-0780-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2034852885</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00034-018-0780-1-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">600</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Xu, Shuiqing</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Uncertainty Inequalities for the Linear Canonical Hilbert Transform</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, LLC, part of Springer Nature 2018</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Uncertainty inequalities</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear canonical Hilbert transform</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear canonical transform</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chai, Yi</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hu, Youqiang</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Feng, Li</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Huang, Lei</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Circuits, systems and signal processing</subfield><subfield code="d">Springer US, 1982</subfield><subfield code="g">37(2018), 10 vom: 07. März, Seite 4584-4598</subfield><subfield code="w">(DE-627)130312134</subfield><subfield code="w">(DE-600)588684-3</subfield><subfield code="w">(DE-576)015889939</subfield><subfield code="x">0278-081X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:37</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:10</subfield><subfield code="g">day:07</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:4584-4598</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00034-018-0780-1</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2244</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">37</subfield><subfield code="j">2018</subfield><subfield code="e">10</subfield><subfield code="b">07</subfield><subfield code="c">03</subfield><subfield code="h">4584-4598</subfield></datafield></record></collection>
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