{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T17:42:58Z","timestamp":1708018978758},"reference-count":33,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,12,13]],"date-time":"2006-12-13T00:00:00Z","timestamp":1165968000000},"content-version":"vor","delay-in-days":5035,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory & Apps"],"published-print":{"date-parts":[[1993,3]]},"abstract":"Abstract<\/jats:title>The elimination of zero\u2010input limit cycles in direct form filter sections using either a rounding or a magnitude truncation fixed\u2010point quantizer is considered. the well\u2010known criterion of Chang is reformulated for second\u2010order filter sections in a more practical form using the bilinear transformation. This enables graphical interpretation and quantitative analysis of the possible error feedback solutions for different pole locations.<\/jats:p>The synthesis of limit\u2010cycle\u2010free error feedback for second\u2010order filter sections is addressed in detail and several solutions are proposed. the error feedback coefficients are constrained to power\u2010of\u2010two values or to symmetric values so that the implementation is efficient, e.g. with signal processors. Different limit\u2010cycle\u2010free solutions are discussed with design examples and their round\u2010off noise properties are compared.<\/jats:p>The absence of limit cycles is related to the round\u2010off noise properties of the filter section. the main conclusion of the paper is that when the EF coefficients are appropriately chosen, low round\u2010off noise and the absence of limit cycles can always be accomplished at the same time. A particularly close correlation between limit cycles and roundoff noise is demonstrated with a rounding quantizer: a limit\u2010cycle\u2010free implementation always guarantees low roundoff noise. For most complex conjugate pole locations the converse relation also holds, i.e. low round\u2010off noise implies the absence of limit cycles.<\/jats:p>","DOI":"10.1002\/cta.4490210204","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T08:21:17Z","timestamp":1183364477000},"page":"141-163","source":"Crossref","is-referenced-by-count":5,"title":["Elimination of limit cycles in direct form digital filters using error feedback"],"prefix":"10.1002","volume":"21","author":[{"given":"Timo I.","family":"Laakso","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,12,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1986.13458"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1975.1162680"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1976.1084254"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1977.1084275"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1987.1086237"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1975.1084033"},{"key":"e_1_2_1_8_2","first-page":"371","article-title":"Suppression of parasitic oscillations in second\u2010order digital filters by means of controlled\u2010rounding arithmetic","volume":"29","author":"Butterweck H.\u2010J.","year":"1975","journal-title":"Arch, Elektron. \u00dcbertragungstech. (Electron. Commun.)"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1977.1084346"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1977.1084345"},{"key":"e_1_2_1_11_2","unstructured":"H. J.Butterweck J. H. F.RitzerfeldandM. J.Werter Finite wordlength effects in digital filters: a review' EUT Report 88\u2010E\u2010205 Faculty of Electrical Engineering Eindhoven University of Technology 1988."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1981.1084956"},{"key":"e_1_2_1_13_2","unstructured":"T.Laakso Elimination of limit cycles in recursive digital filters using error feedback' Proc. Bilkent Int. Conf. on New Trends in Communication Ankara July1990 pp.1073\u20131079."},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","unstructured":"T.Laakso P.DinizandI.Hartimo General criterion for the absence of limit cycles in filter structures with a single quantizer' Proc. Int. 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