Refined linear chirplet transform for time-frequency analysis of non-stationary signals

Time-Frequency Analysis (TFA) stands as a pivotal technique for unraveling the inherent properties of signals, which are omnipresent across natural phenomena. Current methodologies encounter significant challenges in the analysis of non-stationary signals, especially those characterized by closely-spaced or intersecting instantaneous frequencies. In this study, we present the refined linear chirplet transform (RLCT), inspired by the concept of the generalized linear chirplet transform (GLCT), to derive the time-frequency representation of non-stationary signals. By increasing the number of chirp rate searches in GLCT, one can derive higher time-frequency concentration, however, this costs much higher computational resources. In the proposed RLCT, the capacity in searching the optimal chirp rates, or equivalently the rotation angles on the time-frequency plane, is dramatically improved by adopting a local search strategy for mono-component signals. As a sequence, the resolution for the multi- component signals, even with overlapping instantaneous frequency, is greatly enhanced by adopting the idea of the adaptive linear chirplet transform (ALCT), where the components with high energy concentration are consecutively detected and subtracted from consideration. Two critical metrics are employed to assess the performance (accuracy and resolution) of the TFA methods: total energy and energy ratio. The latter is defined as the proportion of energy within a narrowly defined frequency band centered around the actual instantaneous frequency, relative to the total energy. The validation examples demonstrate that the LCT-based methods dramatically enhance the accuracy compared to short-time Fourier transform, in terms of total energy. Furthermore, among the LCT family investigated, the proposed method offers marked improvements in resolution, in terms of energy ratio, while maintaining algorithmic simplicity. The seismic responses of a lighthouse during a severe earthquake are investigated by the RLCT to reveal its frequency drop and recovery due to the opening and closing of the existing cracks.