Chebychev polynomials in a speech recognition model

Abstract

Advanced speech information processing systems require further research on speaker-dependent information. Recently, a specific system of discrete orthogonal polynomials {φ L r ( l); l = 1, 2, …, L} R r =0 has been encountered to play a dominant role in a segmental probability model recently proposed in the speaker-dependent feature extraction from speech waves and applied to text-independent speaker verification. Here, these speech polynomials are shown to be the shifted Chebyshev polynomials on a discrete variable t r ( l − 1, L), whose structural and spectral properties are discussed and reviewed in light of the recent discoveries in the field of discrete orthogonal polynomials.