{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:25:56Z","timestamp":1740147956544,"version":"3.37.3"},"reference-count":26,"publisher":"Wiley","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61172033","61271154"],"award-info":[{"award-number":["61172033","61271154"]}],"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":["61172033","61271154"],"award-info":[{"award-number":["61172033","61271154"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>The study of various living complex systems by system identification method is important, and the identification of the problem is even more challenging when dealing with a dynamic nonlinear system of discrete time. A well-established model based on kernel functions for input of the maximum length sequence (m-sequence) can be used to estimate nonlinear binary kernel slices using cross-correlation method. In this study, we examine the relevant mathematical properties of kernel slices, particularly their shift-and-product property and overlap distortion problem caused by the irregular shifting of the estimated kernel slices in the cross-correlation function between the input m-sequence and the system output. We then derive the properties of the inverse repeat (IR) m-sequence and propose a method of using IR m-sequence as an input to separately estimate odd- and even-order kernel slices to reduce the chance of kernel-slice overlapping. An instance of third-order Wiener nonlinear model is simulated to justify the proposed method.<\/jats:p>","DOI":"10.1155\/2015\/454638","type":"journal-article","created":{"date-parts":[[2015,3,22]],"date-time":"2015-03-22T17:04:23Z","timestamp":1427043863000},"page":"1-9","source":"Crossref","is-referenced-by-count":2,"title":["Identifying Odd\/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences"],"prefix":"10.1155","volume":"2015","author":[{"given":"Jin-yan","family":"Hu","sequence":"first","affiliation":[{"name":"School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9715-9389","authenticated-orcid":true,"given":"Tao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"2004","key":"1"},{"year":"1992","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.clinph.2007.12.004"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.neuro.29.051605.113024"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2006.18.12.3097"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/0378-5955(93)90139-R"},{"issue":"3","key":"7","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1080\/00207176508905543","volume":"2","year":"1965","journal-title":"International Journal of Control"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s11045-004-1677-7"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2005.04.002"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2004.01.003"},{"year":"2007","key":"11"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1097\/AUD.0b013e3182728b88"},{"first-page":"303","volume-title":"A practical nonstochastic approach to nonlinear time-domain analysis","year":"1987","key":"13"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.heares.2008.01.006"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/S0042-6989(01)00078-5"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1109\/10.83603"},{"first-page":"87","volume-title":"An extension of the m-sequence technique for the analysis of multi-input nonlinear systems","year":"1994","key":"17"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/BF02648113"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1109\/TIM.2002.802243"},{"issue":"3","key":"20","first-page":"158","volume":"3","year":"2008","journal-title":"International Journal of Computer Science"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1981.12201"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1021\/ie980761z"},{"issue":"4","key":"23","first-page":"249","volume":"50","year":"2002","journal-title":"Journal of the Audio Engineering Society"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-513-2"},{"issue":"2","key":"25","first-page":"107","volume":"5","year":"1979","journal-title":"Automatica Sinica"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1049\/piee.1970.0048"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2015\/454638.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2015\/454638.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2015\/454638.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,23]],"date-time":"2017-06-23T03:48:13Z","timestamp":1498189693000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/cmmm\/2015\/454638\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":26,"alternative-id":["454638","454638"],"URL":"https:\/\/doi.org\/10.1155\/2015\/454638","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"type":"print","value":"1748-670X"},{"type":"electronic","value":"1748-6718"}],"subject":[],"published":{"date-parts":[[2015]]}}}