Selecting the optimal time-frequency distribution for real-life multicomponent signals under given constraints

Selecting the optimal time-frequency distribution (TFD) for a given real-life signal is one of the major challenges in the field of time-frequency analysis. In this paper, we define a methodology, based on the performance measure for quadratic class of TFDs [1, 2], that allows for such selections to be made for different regions in the time-frequency domain, where specific signal features of interest are located. A TFD which is capable of preserving and enhancing those features, while at the same time it satisfies specific, application-dependent constraints, is selected as the signal optimal TFD for the observed region. The use of this methodology is illustrated on an example of a multicomponent, nonstationary, real-life signal, for which the optimal TFD is required to meet the components' unbiased and efficient instantaneous frequency estimation constraint.