Error sources and error propagation in the Levinson-Durbin algorithm

Papaodysseus Constantin, N; Koukoutsis Elias, B; Triantafyllou Costas, N

dc.contributor.author	Papaodysseus Constantin, N	en
dc.contributor.author	Koukoutsis Elias, B	en
dc.contributor.author	Triantafyllou Costas, N	en
dc.date.accessioned	2014-03-01T01:09:24Z
dc.date.available	2014-03-01T01:09:24Z
dc.date.issued	1993	en
dc.identifier.issn	1053-587X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10954
dc.subject	Error Propagation	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.other	Algorithms	en
dc.subject.other	Numerical stability	en
dc.subject.other	Stability	en
dc.subject.other	Error propagation	en
dc.subject.other	Error sources	en
dc.subject.other	Levinson-Durbin algorithm	en
dc.subject.other	Numerical error	en
dc.subject.other	Iterative methods	en
dc.title	Error sources and error propagation in the Levinson-Durbin algorithm	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/78.212736	en
heal.identifier.secondary	http://dx.doi.org/10.1109/78.212736	en
heal.language	English	en
heal.publicationDate	1993	en
heal.abstract	In this paper, it is proved that there are two types of numerical error, due to finite precision, in the Levinson-Durbin algorithm: an erratic and a systematic one. The erratic one depends on the value the input autocorrelation accidentally takes at an iteration, and, essentially, it affects only the results obtained at this particular recursion. On the contrary, the systematic numerical error increases with the information the system carries and propagates essentially throughout the algorithm. It is shown that, for both types of error, as well as the overall one, there are specific intermediate quantities, calculated in the evolution of the algorithm, which may serve as precise indicators of the exact number of erroneous digits with which the various quantities are computed including the PARCOR's and the filter coefficients. Therefore, the generated numerical error can be accurately traced.	en
heal.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC	en
heal.journalName	IEEE Transactions on Signal Processing	en
dc.identifier.doi	10.1109/78.212736	en
dc.identifier.isi	ISI:A1993LA33600010	en
dc.identifier.volume	41	en
dc.identifier.issue	4	en
dc.identifier.spage	1635	en
dc.identifier.epage	1651	en