{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,18]],"date-time":"2023-11-18T16:28:03Z","timestamp":1700324883357},"reference-count":14,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2001,8,28]],"date-time":"2001-08-28T00:00:00Z","timestamp":998956800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory &amp; Apps"],"published-print":{"date-parts":[[2001,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The cornerstone of the theory of discrete\u2010space single\u2010input\u2013single\u2010output linear systems is the idea that every such system has an input\u2013output map that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which, for the case of bounded inputs mapped continuously into bounded outputs, was recently corrected by adding an additional term to the representation. Here, we give a corresponding corrected result for discrete\u2010space systems with stochastic inputs. Copyright \u00a9 2001 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/cta.164","type":"journal-article","created":{"date-parts":[[2002,8,25]],"date-time":"2002-08-25T19:55:21Z","timestamp":1030305321000},"page":"505-509","source":"Crossref","is-referenced-by-count":2,"title":["A note on representation theorems for linear discrete\u2010space systems with stochastic inputs"],"prefix":"10.1002","volume":"29","author":[{"given":"Irwin W.","family":"Sandberg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2001,8,28]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Circuits, Signals, and Systems","author":"Seibert WM","year":"1997"},{"key":"e_1_2_1_3_2","volume-title":"Signals and Systems","author":"Oppenheim AV","year":"1997"},{"key":"e_1_2_1_4_2","volume-title":"Digital Signal Processing","author":"Proakis JG","year":"1992"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1155\/S1024123X98000878"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2018-3_5"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01206573"},{"key":"e_1_2_1_8_2","unstructured":"SandbergIW.Notes on representation theorems for linear discrete\u2010space systems. Proceedings of the International Symposium on Circuits and Systems Orlando FL May 30\u2013June 2 1999(four pages on CD)."},{"key":"e_1_2_1_9_2","volume-title":"Functional Analysis","author":"Kantorovich LV","year":"1982"},{"key":"e_1_2_1_10_2","volume-title":"Volterra series: engineering fundamentals Dissertation","author":"Boyd SP","year":"1985"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(83)90095-6"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)90373-5"},{"key":"e_1_2_1_13_2","volume-title":"Functional Analysis","author":"Edwards RE","year":"1995"},{"key":"e_1_2_1_14_2","volume-title":"Functional Analysis","author":"Bachman G","year":"1966"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0320-4"}],"container-title":["International Journal of Circuit Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcta.164","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cta.164","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,18]],"date-time":"2023-11-18T15:57:15Z","timestamp":1700323035000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1002\/cta.164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,8,28]]},"references-count":14,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2001,9]]}},"alternative-id":["10.1002\/cta.164"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/cta.164","archive":["Portico"],"relation":{},"ISSN":["0098-9886","1097-007X"],"issn-type":[{"value":"0098-9886","type":"print"},{"value":"1097-007X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,8,28]]}}}