On The Polynomial Approximation for Time-Variant Harmonic Signal Modeling

We present a novel approach to modeling time-variant harmonic content in monophonic audio signals. We show that both amplitude and fundamental frequency time variations can be compactly captured in a single time polynomial which modulates the fundamental harmonic component. A correct estimation of the fundamental frequency is assured through the fully automated spectral analysis method (ASA). The best-fit is easily obtained by linear least-squares, given the fact that the set of equations is linear-in-parameters. In contrast to the existing methods, the proposed approach is designed to properly describe harmonic structures in monophonic audio signals under conditions of both amplitude and frequency variations and low signal-to noise ratios.