Orthogonal Polynomial Representation of Vowels
Jim Young · The Journal of the Acoustical Society of America · 1965
Laguerre and Hermite orthogonal polynomials have been used to approximate single pitch-period segments of 6 vowels produced by each of 2 talkers, one male and one female. Using mean-squared error as a quality criterion, approximation error as a function of polynomial complexity is studied across vowels and talkers. The effect of varying pitch is treated in the manner of time scaling and presented separately. Both polynomial representations permit adjustments of the weighting function used in the computation of coefficients, and the effect of these adjustments is discussed in terms of changes in approximation error. The computer algorithms used for generating the approximating polynomials are presented and possible real-time polynomial analyzers are discussed. [This work was supported by Stanford Research Institute.]