The calculation of the instantaneous frequency using the continuous phase in dynamic matching pursuit algorithm

The instantaneous characteristics of signals,as the priori information,have been introduced into the signal decomposition which can reduce the scanning range of the atomic library and improve the efficiency of the dynamic matching pursuit algorithm.However,when we use the instantaneous phase to obtain the instantaneous frequency,there will be negative frequency without physical meaning and the negative instantaneous frequency can't be applied to matching pursuit.As far as we know,there is no effective solution to overcome the negative instantaneous frequency in matching pursuit. In view of such a situation,the authors,through studying the difference between the principal phase and the unwrapping phase,propose a method to obtain the instantaneous frequency by introducing the continuous phase.Then the formula of calculating continuous phase can be deduced.In the numerical data tests,the authors present the trend graphs that reflect the changes of the three different phases. Finally,the comparison of the instantaneous frequencies obtained by the three phases proves that the instantaneous frequency obtained by the continuous phase avoids the negative anomalies,and hence it is a good choice for matching pursuit algorithm and can be used directly.