Abstract
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 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 but it does not satisfy the marginal properties. The marginal properties are achieved by applying the minimum cross-entropy optimization to the time-frequency distribution. Then, IF may be obtained as the first central moment of this adaptive time-frequency distribution. The proposed method of IF estimation is very powerful for applications with low SNR. A set of real-world and synthetic signals of known IF dynamics is tested with the proposed method as well as with other common time-frequency distributions. The simulation shows that the method successfully extracted the IF of the signals.
Highlights
The instantaneous frequency (IF) of a signal is a parameter of practical importance in situations such as seismic, radar, sonar, communications, and biomedical applications [1, 2, 3, 4]
The purpose of this paper is to explore the best available time-frequency distribution (TFD) for estimating the IF of a signal
The proposed method of extracting the IF of a signal was applied to a set of synthetic signals with known IF laws, and a real-world example of knee joint sound signal
Summary
The instantaneous frequency (IF) of a signal is a parameter of practical importance in situations such as seismic, radar, sonar, communications, and biomedical applications [1, 2, 3, 4]. The importance of the IF concept arises from the fact that in most applications a signal processing engineer is confronted with the task of processing signals whose spectral characteristics (in particular the frequency of the spectral peaks) are varying with time. In this paper the IF is defined by using adaptive time-frequency distribution (TFD). (A detailed review on the fundamentals of IF is available in [1].) It has been shown that the usual way of interpreting the IF as the average frequency at each time brings out unexpected results with Cohen’s class of bilinear TFDs. If the IF is interpreted as the average frequency, the IF need not be a frequency that appears in the spectrum of the signal. The motivation behind this paper is in adaptively constructing a positive TFD suitable for estimating the IF of a signal
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