On the equivalence of phase-based methods for the estimation of instantaneous frequency

Estimating the frequency of sinusoidal components is a key problem in many applications, such as in sinusoidal sound modeling, where the estimation has to be done with a low complexity, on short-term spectra. Many estimators have therefore been proposed in the literature. Among these, we focus in this paper on a class known as the “phase-based” estimators. Despite their different theoretical backgrounds, we prove that four of these estimators are equivalent, at least in theory. We also demonstrate that these estimators perform roughly similarly in practice, however small differences remain which are mainly due to numerical properties of the mathematical operators used in their implementations.