Polynomial bounds for the linear prediction coefficients

Papaodysseus, C; Koukoutsis, E; Carayannis, G

dc.contributor.author	Papaodysseus, C	en
dc.contributor.author	Koukoutsis, E	en
dc.contributor.author	Carayannis, G	en
dc.date.accessioned	2014-03-01T01:08:29Z
dc.date.available	2014-03-01T01:08:29Z
dc.date.issued	1991	en
dc.identifier.issn	0165-1684	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10528
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0026257747&partnerID=40&md5=7e5d19d1f1be04219c6b00000957b647	en
dc.subject	autocorrelation coefficients	en
dc.subject	forward linear prediction, Toeplitz matrices	en
dc.subject	ill-conditioning	en
dc.subject	Linear prediction	en
dc.subject	linear predictors	en
dc.subject	numerical behaviour	en
dc.subject	PARCORs	en
dc.subject	positive definiteness	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.other	Signal Filtering and Prediction	en
dc.subject.other	Signal Processing--Analysis	en
dc.subject.other	Autocorrelation	en
dc.subject.other	Linear prediction	en
dc.subject.other	Polynomials bounds	en
dc.subject.other	Mathematical Techniques	en
dc.title	Polynomial bounds for the linear prediction coefficients	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1991	en
heal.abstract	The purpose of this paper is to introduce a new methodology for the study of the numerical behaviour of the Toeplitz system and the quantities involved in the linear prediction problem. For this reason, first, it is proved that the positive definiteness of the system matrix is equivalent to a set of constraints on the autocorrelation innovation, for which new explicit recursive formulae are given. Next, through these formulae, the minimum bounds of the absolute values of the linear prediction coefficients are computed, which are of the order of P(p/2). However, it is proved that, by imposing proper restrictions on the autocorrelation values, a linear or a polynomial bound of a desired order for the LP coefficients can be obtained. Finally, using the previous analysis, the ill-conditioning of the Toeplitz system and the sensitivity of the determinants of the corresponding matrices are discussed.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Signal Processing	en
dc.identifier.isi	ISI:A1991GT61100008	en
dc.identifier.volume	25	en
dc.identifier.issue	2	en
dc.identifier.spage	215	en
dc.identifier.epage	226	en