An energy-concentrated synchrosqueezing transform using a reassignment operator for the analysis of nonstationary signals

The synchrosqueezing transform (SST) is a novel promising time–frequency analysis (TFA) method that has drawn increasing attention in the signal processing field. Compared with classical TFA methods, SST can provide a higher TF resolution and achieve the decomposition of intrinsic mode function more precisely, which can also benefit various engineering applications, e.g., fault diagnosis of machinery, mechanical intelligent manufacturing, and condition monitoring of machines. However, with the gradual understanding of SST, some drawbacks are recognized. One drawback is that when dealing with strongly frequency-modulated (FM) signals, the SST results smear heavily, which will lead to poor TF resolution and low-accuracy mode decomposition. To solve this problem, we propose a novel method combining the advantages of the SST and reassignment (RS) methods. First, we explore the theory of SST and RS from a geometric perspective and then propose a novel squeezing operator to enhance the TF resolution of SST results based on geometric relationships. Compared with SST, the theoretical analysis shows that the proposed method can provide a more energy-concentrated TF representation and achieve a higher TF resolution. Compared with RS, our proposed method can allow for signal reconstruction and mode decomposition. Numerical and real-world signals are employed to validate the effectiveness of the proposed method, such as bat echo signals, gravitational wave signals, and mechanical vibration signals.