A unified view of non-stationary sinusoidal parameter estimation methods using signal derivatives

In this paper, we present a unified view of three non-stationary sinusoidal parameter estimation methods which are based on taking linear transforms of a signal and its derivatives. These methods, the Distribution Derivative Method (DDM), the Generalized Derivative Method (GDM), and the Generalized Reassignment Method (GRM), are shown to be subcases of a more general method which results in a system of linear equations from which we can solve for the parameter estimators. While the GDM and GRM are known to be theoretically equivalent, we show that they are also equivalent to the DDM in one special case. Matrix formulations are established for the GDM and GRM with a polynomial log-amplitude, polynomial phase sinusoidal signal model, and a bias in previous frequency slope estimators is explicitly demonstrated.