{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T12:35:58Z","timestamp":1775565358336,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,6,4]],"date-time":"2018-06-04T00:00:00Z","timestamp":1528070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2019,1]]},"DOI":"10.1007\/s00034-018-0863-z","type":"journal-article","created":{"date-parts":[[2018,6,4]],"date-time":"2018-06-04T02:15:36Z","timestamp":1528078536000},"page":"395-406","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Uncertainty Principles for the Offset Linear Canonical Transform"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3923-2533","authenticated-orcid":false,"given":"Haiye","family":"Huo","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,6,4]]},"reference":[{"issue":"6","key":"863_CR1","first-page":"1897","volume":"123","author":"W Beckner","year":"1995","unstructured":"W. Beckner, Pitt\u2019s inequality and the uncertainty principle. Proc. Am. Math. Soc. 123(6), 1897\u20131905 (1995)","journal-title":"Proc. Am. Math. Soc."},{"issue":"1","key":"863_CR2","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/0022-247X(85)90140-4","volume":"106","author":"M Benedicks","year":"1985","unstructured":"M. Benedicks, On Fourier transforms of functions supported on sets of finite Lebesgue measure. J. Math. Anal. Appl. 106(1), 180\u2013183 (1985)","journal-title":"J. Math. Anal. Appl."},{"key":"863_CR3","unstructured":"A. Bhandari, A.I. Zayed, Shift-invariant and sampling spaces associated with the special affine Fourier transform. Appl. Comput. Harmon. Anal., 2017 (In Press)"},{"issue":"3","key":"863_CR4","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/BF02649110","volume":"3","author":"GB Folland","year":"1997","unstructured":"G.B. Folland, A. Sitaram, The uncertainty principle: a mathematical survey. J. Fourier Anal. Appl. 3(3), 207\u2013238 (1997)","journal-title":"J. Fourier Anal. Appl."},{"key":"863_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0003-1","volume-title":"Foundations of time-frequency analysis","author":"K Gr\u00f6chenig","year":"2001","unstructured":"K. Gr\u00f6chenig, Foundations of time-frequency analysis (Birkh\u00e4user, Boston, 2001)"},{"key":"863_CR6","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.sigpro.2014.11.021","volume":"111","author":"H Huo","year":"2015","unstructured":"H. Huo, W. Sun, Sampling theorems and error estimates for random signals in the linear canonical transform domain. Signal Process. 111, 31\u201338 (2015)","journal-title":"Signal Process."},{"issue":"6","key":"863_CR7","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s00009-017-1024-5","volume":"14","author":"YE Haoui","year":"2017","unstructured":"Y.E. Haoui, S. Fahlaoui, The uncertainty principle for the two-sided quaternion Fourier transform. Mediterr. J. Math. 14(6), 221 (2017)","journal-title":"Mediterr. J. Math."},{"issue":"3","key":"863_CR8","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1112\/jlms\/s1-8.3.227","volume":"8","author":"GH Hardy","year":"1933","unstructured":"G.H. Hardy, A theorem concerning Fourier transforms. J. London Math. Soc. 8(3), 227\u2013231 (1933)","journal-title":"J. London Math. Soc."},{"key":"863_CR9","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1007\/BF01397280","volume":"43","author":"W Heisenberg","year":"1927","unstructured":"W. Heisenberg, Uber den anschaulichen inhalt der quanten theoretischen kinematik und mechanik. Zeitschrift f\u00fcr Physik 43, 172\u2013198 (1927)","journal-title":"Zeitschrift f\u00fcr Physik"},{"key":"863_CR10","volume-title":"Time-frequency and time-scale methods: Adaptive decompositions, uncertainty principles, and sampling","author":"JA Hogan","year":"2005","unstructured":"J.A. Hogan, J.D. Lakey, Time-frequency and time-scale methods: Adaptive decompositions, uncertainty principles, and sampling (Birkh\u00e4user, Boston, 2005)"},{"issue":"1","key":"863_CR11","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.jat.2007.04.005","volume":"149","author":"P Jaming","year":"2007","unstructured":"P. Jaming, Nazarov\u2019s uncertainty principles in higher dimension. J. Approx. Theory 149(1), 30\u201341 (2007)","journal-title":"J. Approx. Theory"},{"issue":"9","key":"863_CR12","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":"4","key":"863_CR13","first-page":"663","volume":"5","author":"FL Nazarov","year":"1993","unstructured":"F.L. Nazarov, Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type. Algebra I Analiz 5(4), 663\u2013717 (1993)","journal-title":"Algebra I Analiz"},{"issue":"3","key":"863_CR14","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1364\/JOSAA.20.000522","volume":"20","author":"S-C Pei","year":"2003","unstructured":"S.-C. Pei, J.-J. Ding, Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms. JOSA A 20(3), 522\u2013532 (2003)","journal-title":"JOSA A"},{"issue":"1","key":"863_CR15","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s11760-013-0466-x","volume":"8","author":"J Shi","year":"2014","unstructured":"J. Shi, X. Liu, N. Zhang, On uncertainty principles for linear canonical transform of complex signals via operator methods. Signal Image Video Process. 8(1), 85\u201393 (2014)","journal-title":"Signal Image Video Process."},{"issue":"4","key":"863_CR16","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 offset linear canonical transform domains. Signal Image Video Process. 1(4), 359\u2013367 (2007)","journal-title":"Signal Image Video Process."},{"issue":"6","key":"863_CR17","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.1016\/j.sigpro.2010.11.006","volume":"91","author":"R Tao","year":"2011","unstructured":"R. Tao, F. Zhang, Y. Wang, Sampling random signals in a fractional Fourier domain. Signal Process. 91(6), 1394\u20131400 (2011)","journal-title":"Signal Process."},{"issue":"1","key":"863_CR18","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s00034-011-9319-4","volume":"31","author":"D Wei","year":"2012","unstructured":"D. Wei, Q. Ran, Y. Li, A convolution and correlation theorem for the linear canonical transform and its application. Circuits Syst. Signal Process. 31(1), 301\u2013312 (2012)","journal-title":"Circuits Syst. Signal Process."},{"issue":"3","key":"863_CR19","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. 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."},{"key":"863_CR20","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.optcom.2012.10.040","volume":"290","author":"L Xiao","year":"2013","unstructured":"L. Xiao, W. Sun, Sampling theorems for signals periodic in the linear canonical transform domain. Opt. Commun. 290, 14\u201318 (2013)","journal-title":"Opt. Commun."},{"issue":"1","key":"863_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2009\/917354","volume":"2009","author":"G Xu","year":"2009","unstructured":"G. Xu, X. Wang, X. Xu, New inequalities and uncertainty relations on linear canonical transform revisit. EURASIP J. Adv. Signal Process. 2009(1), 1\u20137 (2009)","journal-title":"EURASIP J. Adv. Signal Process."},{"issue":"12","key":"863_CR22","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."},{"issue":"7","key":"863_CR23","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1049\/iet-spr.2015.0514","volume":"10","author":"Q Zhang","year":"2016","unstructured":"Q. Zhang, Zak transform and uncertainty principles associated with the linear canonical transform. IET Signal Process. 10(7), 791\u2013797 (2016)","journal-title":"IET Signal Process."},{"issue":"5","key":"863_CR24","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. Optik 127(5), 2613\u20132616 (2016)","journal-title":"Optik"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-018-0863-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-018-0863-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-018-0863-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,3]],"date-time":"2019-06-03T19:11:58Z","timestamp":1559589118000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-018-0863-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,4]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["863"],"URL":"https:\/\/doi.org\/10.1007\/s00034-018-0863-z","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,4]]},"assertion":[{"value":"26 October 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 May 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}