Enhanced Time-Frequency Representation and Mode Decomposition

Time-frequency representation (TFR) plays a significant role in interpreting and analyzing nonstationary multi-mode signals. However, currently, it is still challenging to handle multi-mode signals with closely-spaced or spectrally-overlapped instantaneous frequencies (IFs), especially under low signal-to-noise ratio (SNR) conditions. To address this issue, we propose an enhanced TFR and mode decomposition (ETFR-MD) method, which is especially suitable to represent and decompose multi-mode signals with such complex IFs. The proposed ETFR-MD method exploits both the IFs and instantaneous amplitudes (IAs) of the signal under investigation. First, we design an initial IF estimation method to deal with overlapped IFs. Then, a low-complexity mode enhancement scheme is proposed so that the enhanced IFs could better fit the underlying IF laws. After that, three alternatives, i.e., short-time Fourier transform (STFT) coefficients, de-chirping, and intrinsic chirp component decomposition (ICCD), are considered for IA recovery. Finally, the extracted IAs are combined with the enhanced IFs to reconstruct each signal mode, respectively. To gain more insights, we quantitatively analyze the interference during mode decomposition and derive the optimal window length for mode separation. Experimental results implemented on both simulated and real-world data confirm the superior performance of the ETFR-MD compared with the state-of-the-art solutions.