Instantaneous frequency estimation via conditional spectral moments and matching pursuit decomposition

The conditional spectral moments are important concepts in signal analysis. In this paper, we decompose a nonstationary signal by use of the matching pursuit algorithm, through using two different types of dictionaries (i.e., the Gaussian and damped sinusoids dictionaries). Then we give expressions for the first and second conditional spectral moments, which are generalizations of the ideas of instantaneous frequency and instantaneous bandwidth. Although in many cases the second conditional moment is not positive and this makes the usual interpretation of this quantity impossible, in this paper we will prove that with matching pursuit decomposition, by using the Gaussian or damped sinusoids dictionaries, the second conditional moment is always positive. In addition, we show that the first moment closely estimates the true instantaneous frequency of the signal.