Encoding sinusoidal amplitudes with a minimum phase rational model

In this paper we present an algorithm for encoding sine wave amplitudes with a minimum phase rational model suitable for harmonic coding applications. Voiced speech frames from different male and female speakers show a very large variation in the number of sinusoids that is present, from more than forty to less than ten in 4 kHz speech. The method we propose involves minimization of the squared error, on a log scale, between this highly variable number of spectral amplitudes and the corresponding values of the magnitude response of a parametric pole-zero model. A weighted iterative approach is used to get very low distortion solutions to this nonlinear problem. This new variable-to-fixed encoding algorithm gives especially impressive results in the case of high pitched female voices, where the number of spectral harmonics is less than the number of parameters in the rational model