Estimating the Instantaneous Frequency of Sinusoidal Components Using Phase-Based Methods

The robust estimation of the frequency of some sinusoidal components is a major prerequisite for many applications, such as in sinusoidal sound modeling, where the estimation often has to be done with low complexity, on short-term spectra. Besides the estimators proposed in the literature, a class known as phase-based estimators is described. It is proven that five of these estimators are equivalent, at least in theory. In-depth practical experiments demonstrate that these estimators perform roughly similarly in practice, although small differences remain, differences that are most probably due to numerical properties of the mathematical operators used in their implementation.