A unified approach for the estimation of instantaneous frequency and its derivatives for non-stationary signals analysis

A unified approach for the estimation of the first three phase derivatives of non-stationary signals is proposed in this paper. The possibility to accurately estimate phase derivatives is important in many applications dealing with objects velocity, acceleration and acceleration rate, such as the radar applications and mechanics. The estimation approach is based on definition of the complex-lag distribution. The proposed distribution is inspired by the concepts of complex analysis theory. The general form of distribution for the estimation of the first, second and third derivative of the phase is derived from the specific individual cases. The theoretical considerations are illustrated in the example with fast varying signal phase function.