Single and Piecewise Polynomials for Modeling of Pitched Sounds

We present a compact approach to simultaneous modeling of non-stationary harmonic and transient components in pitched sound sources. The harmonic and transient components are described by separate models which are built from a common sinusoidal basis modified by a joint action of single and linear piecewise time polynomials respectively. A single polynomial accounts for slow and continuous signal time variations, while various piecewise polynomials can capture fast signal changes on smaller subintervals within the analysis window. The resulting model is linear-in-parameters and the solution to the corresponding linear system of equations provides correct model parameter estimates according to the signal content in the analysis window. The model is extended to deal with mixtures of sounds, where harmonics clustered in a small bandwidth are jointly modeled as a single harmonic. The comparative results suggest that the proposed model outperforms two reference modeling methods in terms of modeling errors and number of parameters.