Determination of the frequency vibrato extent based on the linear predictive coding parameters

Abstract

Many time-domain signals can be modeled as a sum of sinusoids whose main parameters are amplitude and frequency. The frequency can be obtained from the linear predictive coding (LPC) parameters by the pole location in the Z-domain. Although intuition dictates that the amplitude could also be obtained from the LPC parameters, there appears to be no information available that would allow its computation. The purpose of this research is to investigate the relationship between the LPC parameters and the amplitude of a wave in the time domain. In order to accomplish this, the power spectrum obtained using the LPC method was plotted against the FFT spectrum of vibrato samples. They were then compared, and several parameters of the LPC spectrum were changed until both spectra matched. From these matched spectra, the wave amplitude was obtained. This new method was then used in an application to determine the time-varying amplitude of the vibrato wave. This served two purposes: first, to verify the accuracy of the method, and second, to show the usefulness of the time-domain parameters. The results show that there is a direct relationship between the LPC parameters and the amplitude of a wave in the time domain.