Instantaneous mean frequency estimation using adaptive time-frequency distributions

Analysis of non-stationary signals is a challenging task. True non-stationary signal analysis involves monitoring the frequency changes of the signal over time (i.e., monitoring the instantaneous frequency (IF) changes). The IF of a signal is traditionally obtained by taking the first derivative of the phase of the signal with respect to time. This poses some difficulties because the derivative of the phase of the signal may take negative values thus misleading the interpretation of instantaneous frequency. In this paper, a novel approach to extract the IF from its adaptive time-frequency distribution is proposed. The adaptive time-frequency distribution of a signal is obtained by decomposing the signal into components with good time-frequency localization and by combining the Wigner distribution of the components. The adaptive time-frequency distribution thus obtained is free of cross-terms and is a positive time-frequency distribution with good time and frequency localization. The IF may be obtained as the first central moment of the adaptive time-frequency distribution. The proposed method of IF estimation is very powerful for applications with low SNR. The proposed technique was tested with synthetic signals of known IF dynamics, and the method successfully extracted the IF of the signals.