Chebychev polynomials in a speech recognition model

Advanced speech mformatlon processmg systems require further research on speakerdependent mformatlon Recently, a specific system of discrete orthogonal polynomials {4:(l), 1 = 1,2, ,L },“=, has been encountered to play a dommant role m a segmental probability model recently proposed m the speaker-dependent feature extra&on from speech waves and apphed to text-independent speaker verlficatlon Here, these speech polynomrals are shown to be the shifted Chebyshev polynomials on a dtscrete variable t,(l1, L), whose structural and spectral properties are discussed and reviewed m light of the recent discoveries m the field of discrete orthogonal polynomials @ 2001 Elsevler Science Ltd All rights reserved Keywords-Discrete Chebyshev polynomials, Speech recogmtlon, Speaker venficatlon, Speech ldentdicatlon, Speech sound, Speech compression This work has been partially supported by the European ProJect INTAS-93-219-ext and by the Spamsh Dlreccdn General de EnseBnza Superior (DGES) Grant PB-96-0120-C03-01 This work has been partially supported by the European ProJect INTAS-93-219ext, the Junta de Andalucia Grant FQM-207 and by the Spamsh Dlreccdn General de Enseiinza Superior (DGES) Grants PB-96-0120-COl-01 (R A N ) and PB-95-1205 (J S D ) This paper was done durmg the stay of the second author m the Umversldad de Granada 0893-9659/01/s see front matter @ 2001 Elsevler Science Ltd All rights reserved Typeset by .A&-W PI1 SO893-9659(00)00197-X