High-Concentration Time-Frequency Representation and Instantaneous Frequency Estimation of Frequency-Crossing Signals

Frequency-crossing signals are widely found in nature and various engineering systems. Currently, achieving high-resolution time-frequency (TF) representation and accurate instantaneous frequency (IF) estimation for these signals presents a challenge and is a significant area of research. This paper proposes a solution that includes a high-concentration TF representation network and an IF separation and estimation network, designed specifically for analyzing frequency-crossing signals using classical TF analysis and U-net techniques. Through TF data generation, the construction of a U-net, and training, the high-concentration TF representation network achieves high-resolution TF characterization of different frequency-crossing signals. The IF separation and estimation network, with its discriminant model, offers flexibility in determining the number of components within multi-component signals. Following this, the separation network model, with an equal number of components, is utilized for signal separation and IF estimation. Finally, a comparison is performed against the short-time Fourier transform, synchrosqueezing transform, and convolutional neural network. Experimental validation shows that our proposed approach achieves high TF concentration, exhibiting robust noise immunity and enabling precise characterization of the time-varying law of frequency-crossing signals.