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A New Approach for Estimation of Instantaneous Mean Frequency of a TimeVarying Signal
 EURASIP JOURNAL ON APPLIED SIGNAL PROCESSING 2005:17, 2848–2855
, 2005
"... Analysis of nonstationary signals is a challenging task. True nonstationary 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 th ..."
Abstract

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Analysis of nonstationary signals is a challenging task. True nonstationary 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 timefrequency distribution is proposed. The adaptive timefrequency distribution of a signal is obtained by decomposing the signal into components with good timefrequency localization and by combining the Wigner distribution of the components. The adaptive timefrequency distribution thus obtained is free of crossterms and is a positive timefrequency distribution but it does not satisfy the marginal properties. The marginal properties are achieved by applying the minimum crossentropy optimization to the timefrequency distribution. Then, IF may be obtained as the first central moment of this adaptive timefrequency distribution. The proposed method of IF estimation is very powerful for applications with low SNR. A set of realworld and synthetic signals of known IF dynamics is tested with the proposed method as well as with other common timefrequency distributions. The simulation shows that the method successfully extracted the IF of the signals.