{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T21:17:19Z","timestamp":1726003039703},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030033132"},{"type":"electronic","value":"9783030033149"}],"license":[{"start":{"date-parts":[[2018,12,12]],"date-time":"2018-12-12T00:00:00Z","timestamp":1544572800000},"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":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-03314-9_36","type":"book-chapter","created":{"date-parts":[[2018,12,12]],"date-time":"2018-12-12T01:23:41Z","timestamp":1544577821000},"page":"420-432","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Algorithm for Computing the True Discrete Fractional Fourier Transform"],"prefix":"10.1007","author":[{"given":"Dorota","family":"Majorkowska-Mech","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aleksandr","family":"Cariow","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,12,12]]},"reference":[{"key":"36_CR1","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1002\/sapm19298170","volume":"8","author":"N Wiener","year":"1929","unstructured":"Wiener, N.: Hermitian polynomials and Fourier analysis. J. Math. Phys. 8, 70\u201373 (1929)","journal-title":"J. Math. Phys."},{"key":"36_CR2","doi-asserted-by":"crossref","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. J. Inst. Appl. Math. 25, 241\u2013265 (1980)","journal-title":"J. Inst. Appl. Math."},{"issue":"9","key":"36_CR3","doi-asserted-by":"publisher","first-page":"2141","DOI":"10.1109\/78.536672","volume":"44","author":"HM Ozaktas","year":"1996","unstructured":"Ozaktas, H.M., Ankan, O., Kutay, M.A., Bozdagi, G.: Digital computation of the fractional Fourier transform. IEEE Trans. Signal Process. 44(9), 2141\u20132150 (1996). https:\/\/doi.org\/10.1109\/78.536672","journal-title":"IEEE Trans. Signal Process."},{"issue":"4","key":"36_CR4","doi-asserted-by":"publisher","first-page":"994","DOI":"10.1109\/78.492554","volume":"44","author":"B Santhanam","year":"1996","unstructured":"Santhanam, B., McClellan, J.H.: Discrete rotational Fourier transform. IEEE Trans. Signal Process. 44(4), 994\u2013998 (1996). https:\/\/doi.org\/10.1109\/78.492554","journal-title":"IEEE Trans. Signal Process."},{"key":"36_CR5","unstructured":"Pei, S.-C., Yeh, M.-H.: Discrete fractional Fourier transform. In: Proceedings of the IEEE International Symposium on Circuits and Systems, pp. 536\u2013539 (1996)"},{"issue":"6","key":"36_CR6","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1109\/82.686685","volume":"45","author":"S-C Pei","year":"1998","unstructured":"Pei, S.-C., Tseng, C.-C., Yeh, M.-H., Shyu, J.-J.: Discrete fractional Hartley and Fourier transforms. IEEE Trans. Circuits Syst. II Analog. Digit. Signal Process. 45(6), 665\u2013675 (1998). https:\/\/doi.org\/10.1109\/82.686685","journal-title":"IEEE Trans. Circuits Syst. II Analog. Digit. Signal Process."},{"key":"36_CR7","doi-asserted-by":"publisher","unstructured":"Pei, S.-C., Yeh, M.-H.: Discrete fractional Hadamard transform. In: Proceedings of the IEEE International Symposium on Circuits and Systems, vol. 3, pp. 179\u2013182 (1999). https:\/\/doi.org\/10.1109\/ISCAS.1999.778814","DOI":"10.1109\/ISCAS.1999.778814"},{"issue":"11","key":"36_CR8","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1109\/82.885138","volume":"47","author":"S-C Pei","year":"2000","unstructured":"Pei, S.-C., Yeh, M.-H.: Discrete fractional Hilbert transform. IEEE Trans. Circuits Syst. II Analog. Digit. Signal Process. 47(11), 1307\u20131311 (2000). https:\/\/doi.org\/10.1109\/82.885138","journal-title":"IEEE Trans. Circuits Syst. II Analog. Digit. Signal Process."},{"issue":"6","key":"36_CR9","doi-asserted-by":"publisher","first-page":"1198","DOI":"10.1109\/78.923302","volume":"49","author":"S-C Pei","year":"2001","unstructured":"Pei, S.-C., Yeh, M.H.: The discrete fractional cosine and sine transforms. IEEE Trans. Signal Process. 49(6), 1198\u20131207 (2001). https:\/\/doi.org\/10.1109\/78.923302","journal-title":"IEEE Trans. Signal Process."},{"issue":"4\u20136","key":"36_CR10","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.optcom.2005.06.031","volume":"255","author":"Z Liu","year":"2005","unstructured":"Liu, Z., Zhao, H., Liu, S.: A discrete fractional random transform. Opt. Commun. 255(4\u20136), 357\u2013365 (2005). https:\/\/doi.org\/10.1016\/j.optcom.2005.06.031","journal-title":"Opt. Commun."},{"key":"36_CR11","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/S0030-4018(01)01462-6","volume":"197","author":"I\u015e Yetik","year":"2001","unstructured":"Yetik, I.\u015e., Kutay, M.A., Ozaktas, H.M.: Image representation and compression with the fractional Fourier transform. Opt. Commun. 197, 275\u2013278 (2001). https:\/\/doi.org\/10.1016\/S0030-4018(01)01462-6","journal-title":"Opt. Commun."},{"issue":"2","key":"36_CR12","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1006\/jnca.2000.0128","volume":"24","author":"I Djurovi\u0107","year":"2001","unstructured":"Djurovi\u0107, I., Stankovi\u0107, S., Pitas, I.: Digital watermarking in the fractional Fourier transformation domain. J. Netw. Comput. Appl. 24(2), 167\u2013173 (2001). https:\/\/doi.org\/10.1006\/jnca.2000.0128","journal-title":"J. Netw. Comput. Appl."},{"key":"36_CR13","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.optcom.2003.08.030","volume":"226","author":"B Hennelly","year":"2003","unstructured":"Hennelly, B., Sheridan, J.T.: Fractional Fourier transform-based image encryption: phase retrieval algorithm. Opt. Commun. 226, 61\u201380 (2003). https:\/\/doi.org\/10.1016\/j.optcom.2003.08.030","journal-title":"Opt. Commun."},{"issue":"8","key":"36_CR14","doi-asserted-by":"publisher","first-page":"1543","DOI":"10.1007\/s11760-012-0391-4","volume":"8","author":"N Jindal","year":"2014","unstructured":"Jindal, N., Singh, K.: Image and video processing using discrete fractional transforms. Signal Image Video Process. 8(8), 1543\u20131553 (2014). https:\/\/doi.org\/10.1007\/s11760-012-0391-4","journal-title":"Signal Image Video Process."},{"issue":"1","key":"36_CR15","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s11265-009-0401-0","volume":"60","author":"R Tao","year":"2010","unstructured":"Tao, R., Liang, G., Zhao, X.: An efficient FPGA-based implementation of fractional Fourier transform algorithm. J. Signal Process. Syst. 60(1), 47\u201358 (2010). https:\/\/doi.org\/10.1007\/s11265-009-0401-0","journal-title":"J. Signal Process. Syst."},{"issue":"3","key":"36_CR16","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1007\/s11075-014-9862-8","volume":"68","author":"A Cariow","year":"2015","unstructured":"Cariow, A., Majorkowska-Mech, D.: Fast algorithm for discrete fractional Hadamard transform. Numer. Algorithms 68(3), 585\u2013600 (2015). https:\/\/doi.org\/10.1007\/s11075-014-9862-8","journal-title":"Numer. Algorithms"},{"issue":"3","key":"36_CR17","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.acha.2004.02.001","volume":"16","author":"A Bultheel","year":"2004","unstructured":"Bultheel, A., Martinez-Sulbaran, H.E.: Computation of the fractional Fourier transform. Appl. Comput. Harmon. Anal. 16(3), 182\u2013202 (2004)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"11","key":"36_CR18","doi-asserted-by":"crossref","first-page":"1911","DOI":"10.19026\/rjaset.6.3804","volume":"6","author":"M Irfan","year":"2013","unstructured":"Irfan, M., Zheng, L., Shahzad, H.: Review of computing algorithms for discrete fractional Fourier transform. Res. J. Appl. Sci. Eng. Technol. 6(11), 1911\u20131919 (2013)","journal-title":"Res. J. Appl. Sci. Eng. Technol."},{"issue":"14","key":"36_CR19","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1364\/OL.22.001047","volume":"22","author":"S-C Pei","year":"1997","unstructured":"Pei, S.-C., Yeh, M.-H.: Improved discrete fractional Fourier transform. Opt. Lett. 22(14), 1047\u20131049 (1997). https:\/\/doi.org\/10.1364\/OL.22.001047","journal-title":"Opt. Lett."},{"issue":"5","key":"36_CR20","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1109\/78.839980","volume":"48","author":"\u00c7C Candan","year":"2000","unstructured":"Candan, \u00c7.C., Kutay, M.A., Ozaktas, H.M.: The discrete fractional Fourier transform. IEEE Trans. Signal Process. 48(5), 1329\u20131337 (2000). https:\/\/doi.org\/10.1109\/78.839980","journal-title":"IEEE Trans. Signal Process."},{"issue":"10","key":"36_CR21","doi-asserted-by":"publisher","first-page":"4118","DOI":"10.1007\/s00034-017-0503-z","volume":"36","author":"D Majorkowska-Mech","year":"2017","unstructured":"Majorkowska-Mech, D., Cariow, A.: A low-complexity approach to computation of the discrete fractional Fourier transform. Circuits Syst. Signal Process. 36(10), 4118\u20134144 (2017). https:\/\/doi.org\/10.1007\/s00034-017-0503-z","journal-title":"Circuits Syst. Signal Process."},{"key":"36_CR22","doi-asserted-by":"crossref","DOI":"10.1515\/9781400882236","volume-title":"Finite Dimensional Vector Spaces","author":"PR Halmos","year":"1947","unstructured":"Halmos, P.R.: Finite Dimensional Vector Spaces. Princeton University Press, Princeton (1947)"},{"issue":"1","key":"36_CR23","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1109\/TAU.1972.1162342","volume":"20","author":"JH McClellan","year":"1972","unstructured":"McClellan, J.H., Parks, T.W.: Eigenvalue and eigenvector decomposition of the discrete Fourier transform. IEEE Trans. Audio Electroacoust. 20(1), 66\u201374 (1972). https:\/\/doi.org\/10.1109\/TAU.1972.1162342","journal-title":"IEEE Trans. Audio Electroacoust."}],"container-title":["Advances in Intelligent Systems and Computing","Advances in Soft and Hard Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-03314-9_36","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T09:57:00Z","timestamp":1573120620000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-03314-9_36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,12]]},"ISBN":["9783030033132","9783030033149"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-03314-9_36","relation":{},"ISSN":["2194-5357","2194-5365"],"issn-type":[{"type":"print","value":"2194-5357"},{"type":"electronic","value":"2194-5365"}],"subject":[],"published":{"date-parts":[[2018,12,12]]},"assertion":[{"value":"ACS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Multi-Conference on Advanced Computer Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Mi\u0119dzyzdroje","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 September 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 September 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"acs2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/acs.zut.edu.pl","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}