{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T04:50:19Z","timestamp":1754110219262,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,9,17]],"date-time":"2019-09-17T00:00:00Z","timestamp":1568678400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,9,17]],"date-time":"2019-09-17T00:00:00Z","timestamp":1568678400000},"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":"crossref","award":["61861044"],"award-info":[{"award-number":["61861044"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Science Foundation of Yan\u2019an University","award":["YDY2017-05","YDBK2018-36"],"award-info":[{"award-number":["YDY2017-05","YDBK2018-36"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SIViP"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s11760-019-01563-9","type":"journal-article","created":{"date-parts":[[2019,9,17]],"date-time":"2019-09-17T04:07:56Z","timestamp":1568693276000},"page":"351-358","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Fractional convolution, correlation theorem and its application in filter design"],"prefix":"10.1007","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6658-9549","authenticated-orcid":false,"given":"Qiang","family":"Feng","sequence":"first","affiliation":[]},{"given":"Rong-Bo","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,17]]},"reference":[{"key":"1563_CR1","volume-title":"The Fractional Fourier Transform with Applications in Optics and Signal Processing","author":"HM Ozaktas","year":"2001","unstructured":"Ozaktas, H.M., Zalevsky, Z., Kutay, M.A.: The Fractional Fourier Transform with Applications in Optics and Signal Processing. Wiley, New York (2001)"},{"key":"1563_CR2","volume-title":"Linear Canonical Transform and Its Applications","author":"TZ Xu","year":"2013","unstructured":"Xu, T.Z., Li, B.Z.: Linear Canonical Transform and Its Applications. Science Press, Beijing (2013)"},{"issue":"9","key":"1563_CR3","doi-asserted-by":"publisher","first-page":"1875","DOI":"10.1364\/JOSAA.10.001875","volume":"10","author":"D Mendlovic","year":"1993","unstructured":"Mendlovic, D., Ozaktas, H.M.: Fractional Fourier transforms and their optical implementation. J. Opt. Soc. Am. A 10(9), 1875\u20131881 (1993)","journal-title":"J. Opt. Soc. Am. A"},{"issue":"3","key":"1563_CR4","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1093\/imamat\/25.3.241","volume":"25","author":"V Namias","year":"1980","unstructured":"Namias, V.: The fractional order Fourier transform and its application to quantum mechanics. IMA J. Appl. Math. 25(3), 241\u2013265 (1980)","journal-title":"IMA J. Appl. Math."},{"issue":"11","key":"1563_CR5","doi-asserted-by":"publisher","first-page":"3084","DOI":"10.1109\/78.330368","volume":"42","author":"LB Almeida","year":"1994","unstructured":"Almeida, L.B.: The fractional Fourier transform and time\u2013frequency representation. IEEE Trans. Signal Process. 42(11), 3084\u20133091 (1994)","journal-title":"IEEE Trans. Signal Process."},{"issue":"3\u20134","key":"1563_CR6","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1007\/s00006-008-0098-3","volume":"18","author":"E Hitzer","year":"2008","unstructured":"Hitzer, E., Mawardi, B.: Clifford Fourier transform on multivector fields and uncertainty principles for dimensions. Adv. Appl. Clifford Algebr. 18(3\u20134), 715\u2013736 (2008)","journal-title":"Adv. Appl. Clifford Algebr."},{"issue":"2","key":"1563_CR7","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1017\/S0334270000012509","volume":"40","author":"D Mustard","year":"1998","unstructured":"Mustard, D.: Fractional convolution. J. Aust. Math. Soc. Ser. B 40(2), 257\u2013265 (1998)","journal-title":"J. Aust. Math. Soc. Ser. B"},{"key":"1563_CR8","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.optlastec.2013.07.023","volume":"56","author":"XY Lu","year":"2014","unstructured":"Lu, X.Y., Wei, C., Liu, L., Wu, G., Wang, F., Cai, Y.J.: Experimental study of the fractional Fourier transform for a hollow Gaussian beam. Opt. Laser Technol. 56, 92\u201398 (2014)","journal-title":"Opt. Laser Technol."},{"issue":"10","key":"1563_CR9","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1109\/LCOMM.2010.072910.100562","volume":"14","author":"J Zhang","year":"2010","unstructured":"Zhang, J., Wang, Z.: ICI analysis for FRFT-OFDM systems to frequency offset in time\u2013frequency selective fading channels. IEEE Commun. Lett. 14(10), 888\u2013890 (2010)","journal-title":"IEEE Commun. Lett."},{"issue":"4","key":"1563_CR10","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1007\/s11760-018-1399-1","volume":"13","author":"MY Abbass","year":"2019","unstructured":"Abbass, M.Y., Kim, H.W., Abdelwahab, S.A., et al.: Image deconvolution using homomorphic technique. Signal Image Video Process. 13(4), 703\u2013709 (2019)","journal-title":"Signal Image Video Process."},{"key":"1563_CR11","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1016\/j.dsp.2018.09.012","volume":"83","author":"HC Xin","year":"2018","unstructured":"Xin, H.C., Bai, X., Song, Y.E.: ISAR imaging of target with complex motion associated with the fractional Fourier transform. Digital Signal Process. 83, 332\u2013345 (2018)","journal-title":"Digital Signal Process."},{"key":"1563_CR12","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.sigpro.2014.04.009","volume":"107","author":"XP Liu","year":"2015","unstructured":"Liu, X.P., Shi, J., Sha, X.J.: A general framework for sampling and reconstruction in function spaces associated with fractional Fourier transform. Signal Process. 107, 319\u2013326 (2015)","journal-title":"Signal Process."},{"issue":"4","key":"1563_CR13","doi-asserted-by":"publisher","first-page":"1188","DOI":"10.1016\/j.sigpro.2009.10.002","volume":"90","author":"L Durak","year":"2010","unstructured":"Durak, L., Aldirmaz, S.: Adaptive fractional Fourier domain filtering. Signal Process. 90(4), 1188\u20131196 (2010)","journal-title":"Signal Process."},{"issue":"7","key":"1563_CR14","doi-asserted-by":"publisher","first-page":"3541","DOI":"10.1109\/TSP.2007.893931","volume":"55","author":"R Tao","year":"2007","unstructured":"Tao, R., Li, B.Z., Wang, Y.: Spectral analysis and reconstruction for periodic non-uniformly sampled signals in fractional Fourier domain. IEEE Trans. Signal Process. 55(7), 3541\u20133547 (2007)","journal-title":"IEEE Trans. Signal Process."},{"issue":"5","key":"1563_CR15","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1016\/j.sigpro.2008.10.030","volume":"89","author":"BZ Li","year":"2009","unstructured":"Li, B.Z., Xu, T.Z.: The Poisson sum formulae associated with the fractional Fourier transform. Signal Process. 89(5), 851\u2013856 (2009)","journal-title":"Signal Process."},{"issue":"2","key":"1563_CR16","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1049\/iet-spr.2015.0028","volume":"10","author":"Q Feng","year":"2016","unstructured":"Feng, Q., Li, B.Z.: 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":"10","key":"1563_CR17","doi-asserted-by":"publisher","first-page":"3651","DOI":"10.1002\/mma.4251","volume":"40","author":"Q Feng","year":"2017","unstructured":"Feng, Q., Li, B.Z.: Convolution theorem for fractional cosine-sine transform and its application. Math. Methods Appl. Sci. 40(10), 3651\u20133665 (2017)","journal-title":"Math. Methods Appl. Sci."},{"issue":"6","key":"1563_CR18","doi-asserted-by":"publisher","first-page":"1351","DOI":"10.1016\/j.sigpro.2010.10.008","volume":"91","author":"E Sejdic","year":"2011","unstructured":"Sejdic, E., Djurovic, I., Stankovic, L.: Fractional Fourier transform as a signal processing tool: an overview of recent developments. Signal Process. 91(6), 1351\u20131369 (2011)","journal-title":"Signal Process."},{"issue":"5","key":"1563_CR19","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1109\/78.917802","volume":"49","author":"O Akay","year":"2001","unstructured":"Akay, O., Boudreaux-Bartels, G.F.: Fractional convolution and correlation via operator methods and an application to detection of linear FM signals. IEEE Trans. Signal Process. 49(5), 979\u2013993 (2001)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"1563_CR20","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1364\/JOSAA.11.000547","volume":"11","author":"HM Ozaktas","year":"1994","unstructured":"Ozaktas, H.M., Barshan, B., Mendlovic, D., Onural, L.: Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms. J. Opt. Soc. Am. A 11(2), 547\u2013559 (1994)","journal-title":"J. Opt. Soc. Am. A"},{"issue":"4","key":"1563_CR21","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1109\/97.664179","volume":"5","author":"AI Zayed","year":"1998","unstructured":"Zayed, A.I.: A product and convolution theorems for the fractional Fourier transform. IEEE Signal Process. Lett. 5(4), 101\u2013103 (1998)","journal-title":"IEEE Signal Process. Lett."},{"issue":"10","key":"1563_CR22","doi-asserted-by":"publisher","first-page":"2804","DOI":"10.1109\/78.720382","volume":"46","author":"P Kraniauskas","year":"1998","unstructured":"Kraniauskas, P., Cariolaro, G., Erseghe, T.: Method for defining a class of fractional operations. IEEE Trans. Signal Process. 46(10), 2804\u20132807 (1998)","journal-title":"IEEE Trans. Signal Process."},{"issue":"6","key":"1563_CR23","doi-asserted-by":"publisher","first-page":"1976","DOI":"10.1016\/j.sigpro.2009.12.016","volume":"90","author":"R Torres","year":"2010","unstructured":"Torres, R., Pellat-Finet, P., Torres, Y.: Fractional convolution, fractional correlation and their translation invariance properties. Signal Process. 90(6), 1976\u20131984 (2010)","journal-title":"Signal Process."},{"issue":"1","key":"1563_CR24","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.optcom.2007.06.022","volume":"278","author":"KK Sharma","year":"2007","unstructured":"Sharma, K.K., Joshi, S.D.: Papoulis-like generalized sampling expansions in fractional Fourier domains and their application to superresolution. Opt. Commun. 278(1), 52\u201359 (2007)","journal-title":"Opt. Commun."},{"issue":"1","key":"1563_CR25","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1109\/97.551689","volume":"4","author":"LB Almeida","year":"1997","unstructured":"Almeida, L.B.: Product and convolution theorems for the fractional Fourier transform. IEEE Signal Process. Lett. 4(1), 15\u201317 (1997)","journal-title":"IEEE Signal Process. Lett."},{"issue":"11","key":"1563_CR26","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1109\/LSP.2010.2071383","volume":"17","author":"J Shi","year":"2010","unstructured":"Shi, J., Chi, Y.G., Zhang, N.T.: Multichannel sampling and reconstruction of bandlimited signals in fractional Fourier domain. IEEE Signal Process. Lett. 17(11), 909\u2013912 (2010)","journal-title":"IEEE Signal Process. Lett."},{"issue":"1","key":"1563_CR27","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s11277-011-0235-5","volume":"65","author":"AK Singh","year":"2012","unstructured":"Singh, A.K., Saxena, R.: On convolution and product theorems for Frft. Wirel. Pers. Commun. 65(1), 189\u2013201 (2012)","journal-title":"Wirel. Pers. Commun."},{"issue":"3","key":"1563_CR28","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1007\/s11760-011-0261-5","volume":"7","author":"DY Wei","year":"2013","unstructured":"Wei, D.Y., Ran, Q.W.: Multiplicative filtering in the fractional Fourier domain. Signal Image Video Process. 7(3), 575\u2013580 (2013)","journal-title":"Signal Image Video Process."},{"issue":"13","key":"1563_CR29","doi-asserted-by":"publisher","first-page":"1340","DOI":"10.1002\/wcm.2254","volume":"14","author":"J Shi","year":"2014","unstructured":"Shi, J., Sha, X.J., Song, X.C.: Generalized convolution theorem associated with fractional Fourier transform. Wirel. Commun. Mob. Comput. 14(13), 1340\u20131351 (2014)","journal-title":"Wirel. Commun. Mob. Comput."},{"issue":"7","key":"1563_CR30","doi-asserted-by":"publisher","first-page":"3669","DOI":"10.1016\/j.ijleo.2015.12.069","volume":"127","author":"DY Wei","year":"2016","unstructured":"Wei, D.Y.: Novel convolution and correlation theorems for the fractional Fourier transform. Int. J. Light Electron Opt. 127(7), 3669\u20133675 (2016)","journal-title":"Int. J. Light Electron Opt."},{"issue":"2","key":"1563_CR31","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1007\/s11277-016-3567-3","volume":"92","author":"PK Anh","year":"2017","unstructured":"Anh, P.K., Castro, L.P., Thao, P.T.: Two new convolutions for the fractional Fourier transform. Wirel. Pers. Commun. 92(2), 623\u2013637 (2017)","journal-title":"Wirel. Pers. Commun."},{"issue":"2","key":"1563_CR32","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1364\/AO.34.000303","volume":"34","author":"D Mendlovic","year":"1995","unstructured":"Mendlovic, D., OzaktasA, H.M., Lohmann, A.W.: Fractional correlation. Appl. Opt. 34(2), 303\u2013309 (1995)","journal-title":"Appl. Opt."},{"key":"1563_CR33","unstructured":"Akay, O.: Unitary and Hermitian fractional operators and their extensions: fractional Mellin transform, joint fractional representations and fractional correlations. Kingston: PhD thesis, University of Rhode Island (2000)"},{"issue":"10","key":"1563_CR34","doi-asserted-by":"publisher","first-page":"2269","DOI":"10.1109\/78.469861","volume":"43","author":"RG Baraniuk","year":"1995","unstructured":"Baraniuk, R.G., Jones, D.L.: Unitary equivalence: a new twist on signal processing. IEEE Trans. Signal Process. 43(10), 2269\u20132282 (1995)","journal-title":"IEEE Trans. Signal Process."},{"issue":"6","key":"1563_CR35","doi-asserted-by":"publisher","first-page":"1365","DOI":"10.1109\/78.506604","volume":"44","author":"AM Sayeed","year":"1996","unstructured":"Sayeed, A.M., Jones, D.L.: Integral transforms covariant to unitary operators and their implications for joint signal representations. IEEE Trans. Signal Process. 44(6), 1365\u20131377 (1996)","journal-title":"IEEE Trans. Signal Process."},{"key":"1563_CR36","volume-title":"Fourier Transforms","author":"IN Sneddon","year":"1951","unstructured":"Sneddon, I.N.: Fourier Transforms. McGray-Hill, New York (1951)"},{"key":"1563_CR37","first-page":"31","volume":"1","author":"VA Kakichev","year":"1998","unstructured":"Kakichev, V.A., Thao, N.X.: On a constructive method for the generalized integral convolution (in Russian). Izv. Vyss. Uchebnykh Zaved. Math. 1, 31\u201340 (1998)","journal-title":"Izv. Vyss. Uchebnykh Zaved. Math."},{"issue":"5","key":"1563_CR38","doi-asserted-by":"publisher","first-page":"592","DOI":"10.1007\/s11432-006-2016-4","volume":"49","author":"B Deng","year":"2006","unstructured":"Deng, B., Tao, R., Wang, Y.: Convolution theorem for the linear canonical transform and their applications. Sci. China Inf. Sci. 49(5), 592\u2013603 (2006)","journal-title":"Sci. China Inf. Sci."}],"container-title":["Signal, Image and Video Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11760-019-01563-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11760-019-01563-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11760-019-01563-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T23:18:58Z","timestamp":1600211938000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11760-019-01563-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,17]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["1563"],"URL":"https:\/\/doi.org\/10.1007\/s11760-019-01563-9","relation":{},"ISSN":["1863-1703","1863-1711"],"issn-type":[{"type":"print","value":"1863-1703"},{"type":"electronic","value":"1863-1711"}],"subject":[],"published":{"date-parts":[[2019,9,17]]},"assertion":[{"value":"12 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 July 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}