{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,30]],"date-time":"2025-11-30T09:14:12Z","timestamp":1764494052464,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T00:00:00Z","timestamp":1564963200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T00:00:00Z","timestamp":1564963200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51577046","51637004"],"award-info":[{"award-number":["51577046","51637004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61633005","61673076"],"award-info":[{"award-number":["61633005","61673076"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["JZ2018HGTA0216","JZ2018HGBZ0099"],"award-info":[{"award-number":["JZ2018HGTA0216","JZ2018HGBZ0099"]}]},{"name":"the National Key Research and Development Plan: Important Scientific Instruments and Equipment Development","award":["2016YFF0102200"],"award-info":[{"award-number":["2016YFF0102200"]}]},{"name":"Equipment research project in advance","award":["41402040301"],"award-info":[{"award-number":["41402040301"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s00034-019-01217-8","type":"journal-article","created":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T14:02:53Z","timestamp":1565013773000},"page":"1699-1712","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Extrapolation Theorem for Bandlimited Signals Associated with the Offset Linear Canonical Transform"],"prefix":"10.1007","volume":"39","author":[{"given":"Shuiqing","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Feng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Chai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bingbing","family":"Dong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingying","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yigang","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,8,5]]},"reference":[{"issue":"22","key":"1217_CR1","doi-asserted-by":"publisher","first-page":"1801","DOI":"10.1364\/OL.19.001801","volume":"19","author":"S Abe","year":"1994","unstructured":"S. Abe, J.T. Sheridan, Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation. Opt. Lett. 19(22), 1801\u20131803 (1994)","journal-title":"Opt. Lett."},{"issue":"11","key":"1217_CR2","doi-asserted-by":"publisher","first-page":"3084","DOI":"10.1109\/78.330368","volume":"42","author":"L Almeida","year":"1994","unstructured":"L. Almeida, The fractional fourier transform and time-frequency representations. IEEE Trans. Signal Process. 42(11), 3084\u20133091 (1994)","journal-title":"IEEE Trans. Signal Process."},{"issue":"7","key":"1217_CR3","doi-asserted-by":"publisher","first-page":"2471","DOI":"10.1007\/s00034-015-0146-x","volume":"35","author":"YJ Cao","year":"2016","unstructured":"Y.J. Cao, B.Z. Li, Y.G. Li, Y.H. Chen, Logarithmic uncertainty relations for odd or even signals associate with Wigner\u2013Ville distribution. Circuits Syst. Signal Process. 35(7), 2471\u20132486 (2016)","journal-title":"Circuits Syst. Signal Process."},{"issue":"2","key":"1217_CR4","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1049\/iet-spr.2015.0028","volume":"10","author":"LBZ Feng Qiang","year":"2016","unstructured":"L.B.Z. Feng Qiang, Convolution and correlation theorems for the two-dimensional linear canonical transform and its applications. IET Signal Process. 10(2), 125\u2013132 (2016)","journal-title":"IET Signal Process."},{"issue":"4","key":"1217_CR5","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1109\/TASSP.1981.1163639","volume":"29","author":"A Jain","year":"1981","unstructured":"A. Jain, S. Ranganath, Extrapolation algorithms for discrete signals with application in spectral estimation. IEEE Trans. Acoust. Speech Signal Process. 29(4), 830\u2013845 (1981)","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"issue":"4\u20136","key":"1217_CR6","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/0030-4018(95)00708-3","volume":"126","author":"DF James","year":"1996","unstructured":"D.F. James, G.S. Agarwal, The generalized Fresnel transform and its application to optics. Opt. Commun. 126(4\u20136), 207\u2013212 (1996)","journal-title":"Opt. Commun."},{"issue":"9","key":"1217_CR7","doi-asserted-by":"publisher","first-page":"1028","DOI":"10.1002\/mma.2657","volume":"36","author":"K Kou","year":"2013","unstructured":"K. Kou, J. Morais, Y. Zhang, Generalized prolate spheroidal wave functions for offset linear canonical transform in Clifford analysis. Math. Methods Appl. Sci. 36(9), 1028\u20131041 (2013)","journal-title":"Math. Methods Appl. Sci."},{"issue":"8","key":"1217_CR8","doi-asserted-by":"publisher","first-page":"1772","DOI":"10.1063\/1.1665805","volume":"12","author":"M Moshinsky","year":"1971","unstructured":"M. Moshinsky, Linear canonical transformations and their unitary representations. J. Math. Phys. 12(8), 1772\u20131780 (1971)","journal-title":"J. Math. Phys."},{"issue":"4","key":"1217_CR9","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/BF02570568","volume":"4","author":"MZ Nashed","year":"1991","unstructured":"M.Z. Nashed, G.G. Walter, General sampling theorems for functions in reproducing kernel Hilbert spaces. Math. Control Signals Syst. 4(4), 363 (1991)","journal-title":"Math. Control Signals Syst."},{"issue":"3","key":"1217_CR10","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1364\/JOSAA.20.000522","volume":"20","author":"SC Pei","year":"2003","unstructured":"S.C. Pei, J.J. Ding, Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms. J. Opt. Soc. Am. Opt. Image Sci. Vis. 20(3), 522\u201332 (2003)","journal-title":"J. Opt. Soc. Am. Opt. Image Sci. Vis."},{"issue":"2","key":"1217_CR11","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1109\/PROC.1970.7598","volume":"58","author":"CL Rino","year":"1970","unstructured":"C.L. Rino, The application of prolate spheroidal wave functions to the detection and estimation of band-limited signals. Proc. IEEE 58(2), 248\u2013249 (1970)","journal-title":"Proc. IEEE"},{"issue":"2","key":"1217_CR12","doi-asserted-by":"publisher","first-page":"454","DOI":"10.1016\/j.optcom.2006.03.062","volume":"265","author":"KK Sharma","year":"2006","unstructured":"K.K. Sharma, S.D. Joshi, Signal separation using linear canonical and fractional Fourier transforms. Opt. Commun. 265(2), 454\u2013460 (2006)","journal-title":"Opt. Commun."},{"issue":"24","key":"1217_CR13","doi-asserted-by":"publisher","first-page":"6379","DOI":"10.1109\/TSP.2016.2602808","volume":"64","author":"J Shi","year":"2016","unstructured":"J. Shi, X. Liu, L. He, M. Han, Q. Li, N. Zhang, Sampling and reconstruction in arbitrary measurement and approximation spaces associated with linear canonical transform. IEEE Trans. Signal Process. 64(24), 6379\u20136391 (2016)","journal-title":"IEEE Trans. Signal Process."},{"key":"1217_CR14","first-page":"1","volume":"99","author":"J Shi","year":"2017","unstructured":"J. Shi, X. Liu, F.G. Yan, W. Song, Error analysis of reconstruction from linear canonical transform-based sampling. IEEE Trans. Signal Process. 99, 1\u20131 (2017)","journal-title":"IEEE Trans. Signal Process."},{"issue":"3","key":"1217_CR15","doi-asserted-by":"publisher","first-page":"1502","DOI":"10.1109\/TSP.2011.2176338","volume":"60","author":"J Shi","year":"2012","unstructured":"J. Shi, X. Sha, Q. Zhang, N. Zhang, Extrapolation of bandlimited signals in linear canonical transform domain. IEEE Trans. Signal Process. 60(3), 1502\u20131508 (2012)","journal-title":"IEEE Trans. Signal Process."},{"issue":"1","key":"1217_CR16","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1002\/j.1538-7305.1961.tb03976.x","volume":"40","author":"D Slepian","year":"2014","unstructured":"D. Slepian, H.O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty\u2013i. Bell Labs Tech. J. 40(1), 43\u201363 (2014)","journal-title":"Bell Labs Tech. J."},{"issue":"4","key":"1217_CR17","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s11760-007-0029-0","volume":"1","author":"A Stern","year":"2007","unstructured":"A. Stern, Sampling of compact signals in the offset linear canonical domains. Signal Image Video Process. 1(4), 359\u2013367 (2007)","journal-title":"Signal Image Video Process."},{"key":"1217_CR18","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/j.ijleo.2017.08.099","volume":"157","author":"D Urynbassarova","year":"2018","unstructured":"D. Urynbassarova, B.Z. Li, R. Tao, Convolution and correlation theorems for Wigner-Ville distribution associated with the offset linear canonical transform. Opt. Int. J. Light Electron. Opt. 157, 455\u2013466 (2018)","journal-title":"Opt. Int. J. Light Electron. Opt."},{"key":"1217_CR19","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.ijleo.2018.02.111","volume":"164","author":"D Wei","year":"2018","unstructured":"D. Wei, New product and correlation theorems for the offset linear canonical transform and its applications. Optik 164, 243\u2013253 (2018)","journal-title":"Optik"},{"issue":"6","key":"1217_CR20","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1049\/iet-spr.2013.0240","volume":"8","author":"D Wei","year":"2014","unstructured":"D. Wei, Y. Li, Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain. IET Signal Process. 8(6), 647\u2013657 (2014)","journal-title":"IET Signal Process."},{"issue":"3","key":"1217_CR21","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1007\/s11760-012-0342-0","volume":"8","author":"Q Xiang","year":"2014","unstructured":"Q. Xiang, K.Y. Qin, Convolution, correlation, and sampling theorems for the offset linear canonical transform. Signal Image Video Process. 8(3), 433\u2013442 (2014)","journal-title":"Signal Image Video Process."},{"issue":"5","key":"1217_CR22","doi-asserted-by":"publisher","first-page":"2385","DOI":"10.1007\/s00034-013-9575-6","volume":"32","author":"Q Xiang","year":"2013","unstructured":"Q. Xiang, K.Y. Qin, Q.Z. Huang, Multichannel sampling of signals band-limited in offset linear canonical transform domains. Circuits Syst. Signal Process. 32(5), 2385\u20132406 (2013)","journal-title":"Circuits Syst. Signal Process."},{"issue":"12","key":"1217_CR23","doi-asserted-by":"publisher","first-page":"3979","DOI":"10.1007\/s00034-015-0053-1","volume":"34","author":"S Xu","year":"2015","unstructured":"S. Xu, Y. Chai, Y. Hu, Spectral analysis of sampled band-limited signals in the offset linear canonical transform domain. Circuits Syst. Signal Process. 34(12), 3979\u20133997 (2015)","journal-title":"Circuits Syst. Signal Process."},{"key":"1217_CR24","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.optcom.2015.03.027","volume":"348","author":"S Xu","year":"2015","unstructured":"S. Xu, Y. Chai, Y. Hu, C. Jiang, Y. Li, Reconstruction of digital spectrum from periodic nonuniformly sampled signals in offset linear canonical transform domain. Opt. Commun. 348, 59\u201365 (2015)","journal-title":"Opt. Commun."},{"key":"1217_CR25","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.aeue.2017.07.001","volume":"81","author":"S Xu","year":"2017","unstructured":"S. Xu, L. Feng, Y. Chai, Y. Hu, L. Huang, Sampling theorems for bandlimited random signals in the offset linear canonical transform domain. AEU Int. J. Electron. Commun. 81, 114\u2013119 (2017)","journal-title":"AEU Int. J. Electron. Commun."},{"key":"1217_CR26","first-page":"1","volume":"11","author":"S Xu","year":"2018","unstructured":"S. Xu, L. Huang, Y. Chai, Y. He, Nonuniform sampling theorems for bandlimited signals in the offset linear canonical transform. Circuits Syst. Signal Process. 11, 1\u201318 (2018)","journal-title":"Circuits Syst. Signal Process."},{"issue":"8","key":"1217_CR27","first-page":"1","volume":"2018","author":"S Xu","year":"2018","unstructured":"S. Xu, Z. Ke, C. Yi, Y. He, F. Li, Gear fault diagnosis in variable speed condition based on multiscale chirplet path pursuit and linear canonical transform. Complexity 2018(8), 1\u20138 (2018)","journal-title":"Complexity"},{"issue":"4","key":"1217_CR28","doi-asserted-by":"publisher","first-page":"1750031","DOI":"10.1142\/S021969131750031X","volume":"15","author":"S Xu","year":"2017","unstructured":"S. Xu, F. Li, C. Yi, Y. Hu, L. Huang, The properties of generalized offset linear canonical Hilbert transform and its applications. Int. J. Wavelets Multiresolut. Inf. Process. 15(4), 1750031 (2017)","journal-title":"Int. J. Wavelets Multiresolut. Inf. Process."},{"issue":"1","key":"1217_CR29","doi-asserted-by":"publisher","first-page":"1795","DOI":"10.1186\/s40064-016-3479-4","volume":"5","author":"S Xu","year":"2016","unstructured":"S. Xu, C. Yi, Y. Hu, H. Lei, F. Li, The analysis of decimation and interpolation in the linear canonical transform domain. SpringerPlus 5(1), 1795 (2016)","journal-title":"SpringerPlus"},{"key":"1217_CR30","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.sigpro.2017.09.008","volume":"143","author":"YN Zhang","year":"2018","unstructured":"Y.N. Zhang, B.Z. Li, $$\\phi $$-linear canonical analytic signals. Signal Process. 143, 181\u2013190 (2018)","journal-title":"Signal Process."},{"key":"1217_CR31","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.sigpro.2015.06.010","volume":"118","author":"ZC Zhang","year":"2016","unstructured":"Z.C. Zhang, New Wigner distribution and ambiguity function based on the generalized translation in the linear canonical transform domain. Signal Process. 118, 51\u201361 (2016)","journal-title":"Signal Process."},{"key":"1217_CR32","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.dsp.2017.06.016","volume":"69","author":"ZC Zhang","year":"2017","unstructured":"Z.C. Zhang, Tighter uncertainty principles for linear canonical transform in terms of matrix decomposition. Digit. Signal Process. 69, 70\u201385 (2017)","journal-title":"Digit. Signal Process."},{"key":"1217_CR33","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.sigpro.2014.02.002","volume":"101","author":"H Zhao","year":"2014","unstructured":"H. Zhao, R. Wang, D. Song, T. Zhang, Y. Liu, Unified approach to extrapolation of bandlimited signals in linear canonical transform domain. Signal Process. 101, 65\u201373 (2014)","journal-title":"Signal Process."},{"issue":"12","key":"1217_CR34","doi-asserted-by":"publisher","first-page":"2631","DOI":"10.1364\/JOSAA.31.002631","volume":"31","author":"L Zhao","year":"2014","unstructured":"L. Zhao, J.J. Healy, J.T. Sheridan, Two-dimensional nonseparable linear canonical transform: sampling theorem and unitary discretization. J. Opt. Soc. Am A Opt. Image Sci. Vis. 31(12), 2631\u20132641 (2014)","journal-title":"J. Opt. Soc. Am A Opt. Image Sci. Vis."},{"issue":"5","key":"1217_CR35","doi-asserted-by":"publisher","first-page":"2613","DOI":"10.1016\/j.ijleo.2015.11.211","volume":"127","author":"X Zhi","year":"2016","unstructured":"X. Zhi, D. Wei, W. Zhang, A generalized convolution theorem for the special affine Fourier transform and its application to filtering. Opt. Int. J. Light Electron Opt. 127(5), 2613\u20132616 (2016)","journal-title":"Opt. Int. J. Light Electron Opt."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-019-01217-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-019-01217-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-019-01217-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T23:21:21Z","timestamp":1596496881000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-019-01217-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,5]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["1217"],"URL":"https:\/\/doi.org\/10.1007\/s00034-019-01217-8","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2019,8,5]]},"assertion":[{"value":"18 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 July 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 July 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 August 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}