Optimal Field Sampling of Arc Sources via Asymptotic Study of the Radiation Operator
In this paper, the question of how to efficiently sample the field radiated by a circumference arc source is addressed. Classical sampling strategies require the acquisition of a redundant number of field measurements that can make the acquisition time prohibitive. For such reason, the paper aims at...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/11/2/270 |
| _version_ | 1797494483436175360 |
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| author | Raffaele Moretta Giovanni Leone Fortuna Munno Rocco Pierri |
| author_facet | Raffaele Moretta Giovanni Leone Fortuna Munno Rocco Pierri |
| author_sort | Raffaele Moretta |
| collection | DOAJ |
| description | In this paper, the question of how to efficiently sample the field radiated by a circumference arc source is addressed. Classical sampling strategies require the acquisition of a redundant number of field measurements that can make the acquisition time prohibitive. For such reason, the paper aims at finding the minimum number of basis functions representing the radiated field with good accuracy and at providing an interpolation formula of the radiated field that exploits a non-redundant number of field samples. To achieve the first task, the number of relevant singular values of the radiation operator is computed by exploiting a weighted adjoint operator. In particular, the kernel of the related eigenvalue problem is first evaluated asymptotically; then, a warping transformation and a proper choice of the weight function are employed to recast such a kernel as a convolution and bandlimited function of sinc type. Finally, the number of significant singular values of the radiation operator is found by invoking the Slepian–Pollak results. The second task is achieved by exploiting a Shannon sampling expansion of the reduced field. The analysis is developed for both the far and the near fields radiated by a 2D scalar arc source observed on a circumference arc. |
| first_indexed | 2024-03-10T01:34:57Z |
| format | Article |
| id | doaj.art-d9439c27aaa549f7ba64a54f725d63a1 |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T01:34:57Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-d9439c27aaa549f7ba64a54f725d63a12023-11-23T13:35:01ZengMDPI AGElectronics2079-92922022-01-0111227010.3390/electronics11020270Optimal Field Sampling of Arc Sources via Asymptotic Study of the Radiation OperatorRaffaele Moretta0Giovanni Leone1Fortuna Munno2Rocco Pierri3Dipartimento di Ingegneria, Università della Campania “Lugi Vanvitelli”, Via Roma 29, 81031 Aversa, ItalyDipartimento di Ingegneria, Università della Campania “Lugi Vanvitelli”, Via Roma 29, 81031 Aversa, ItalyDipartimento di Ingegneria, Università della Campania “Lugi Vanvitelli”, Via Roma 29, 81031 Aversa, ItalyDipartimento di Ingegneria, Università della Campania “Lugi Vanvitelli”, Via Roma 29, 81031 Aversa, ItalyIn this paper, the question of how to efficiently sample the field radiated by a circumference arc source is addressed. Classical sampling strategies require the acquisition of a redundant number of field measurements that can make the acquisition time prohibitive. For such reason, the paper aims at finding the minimum number of basis functions representing the radiated field with good accuracy and at providing an interpolation formula of the radiated field that exploits a non-redundant number of field samples. To achieve the first task, the number of relevant singular values of the radiation operator is computed by exploiting a weighted adjoint operator. In particular, the kernel of the related eigenvalue problem is first evaluated asymptotically; then, a warping transformation and a proper choice of the weight function are employed to recast such a kernel as a convolution and bandlimited function of sinc type. Finally, the number of significant singular values of the radiation operator is found by invoking the Slepian–Pollak results. The second task is achieved by exploiting a Shannon sampling expansion of the reduced field. The analysis is developed for both the far and the near fields radiated by a 2D scalar arc source observed on a circumference arc.https://www.mdpi.com/2079-9292/11/2/270field samplingnumber of degrees of freedom (NDF)singular values decomposition (SVD)conformal source |
| spellingShingle | Raffaele Moretta Giovanni Leone Fortuna Munno Rocco Pierri Optimal Field Sampling of Arc Sources via Asymptotic Study of the Radiation Operator Electronics field sampling number of degrees of freedom (NDF) singular values decomposition (SVD) conformal source |
| title | Optimal Field Sampling of Arc Sources via Asymptotic Study of the Radiation Operator |
| title_full | Optimal Field Sampling of Arc Sources via Asymptotic Study of the Radiation Operator |
| title_fullStr | Optimal Field Sampling of Arc Sources via Asymptotic Study of the Radiation Operator |
| title_full_unstemmed | Optimal Field Sampling of Arc Sources via Asymptotic Study of the Radiation Operator |
| title_short | Optimal Field Sampling of Arc Sources via Asymptotic Study of the Radiation Operator |
| title_sort | optimal field sampling of arc sources via asymptotic study of the radiation operator |
| topic | field sampling number of degrees of freedom (NDF) singular values decomposition (SVD) conformal source |
| url | https://www.mdpi.com/2079-9292/11/2/270 |
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