Adaptive Linear Chirplet Transform for Analyzing Signals With Crossing Frequency Trajectories

Signal time-frequency analysis is widely used in industrial fields, for example, machinery fault diagnosis. Current methods cannot well address the multicomponents’ signals with crossing frequency trajectories. For example, the adaptive decomposition methods have a mode-mixing problem. The linear transforms have smear problems due to the mutual interference caused by crossing frequencies. To address these issues, in this article, we propose an iterative approach named adaptive linear chirplet transform (ALCT). It works by calculating the signal linear chirplet transform (LCT) with a series of chirp rates as parameters, iteratively estimating the characteristics of the signal mode with the highest amplitude in the residual LCT and updating the residual LCT by removing the LCT of the detected mode, and constructing the signal time-frequency representation (TFR) based on the estimated characteristics of the detected modes. The ALCT can clearly reveal the TFRs of signals with crossing frequency trajectories. It does not have the frequency estimation errors caused by mode mixing and avoids the mutual interference of the crossing frequencies. It is efficient, as it can obtain the LCT of the detected mode by directly weighting and shifting the LCT reference. The effectiveness of the ALCT is validated using simulations and real-world signals.