Effect of model mismatch on polynomial envelope and phase modeling of nonstationary sinusoids

In this paper we examine the effect of model mismatch when modeling a signal consisting of multiple non-stationary sinusoids. The envelopes and frequencies of the components were modeled as polynomials of low order over short intervals of time and the coefficients estimated using the least-squares error criterion. If the block length and model orders are not properly chosen, unacceptable errors occurred in the estimated frequency tracks. The errors tended to increase as the number of components increased. Using the simpler constant envelope, constant frequency sinewave model for short, heavily overlapping blocks and smoothing the resulting frequency tracks gave surprisingly good results when analyzing a long duration multicomponent signal. We conclude that the more complex polynomial model may not always yield the expected increase in accuracy in signal modeling