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.

中文翻译：

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用于非平稳信号时频分析的精细线性线性调频变换


时频分析 (TFA) 是揭示信号固有特性的关键技术，信号在自然现象中无处不在。当前的方法在分析非平稳信号时遇到重大挑战，特别是那些具有紧密间隔或交叉瞬时频率特征的信号。在本研究中，受广义线性调频变换（GLCT）概念的启发，我们提出了精炼线性调频变换（RLCT），以推导非平稳信号的时频表示。通过增加 GLCT 中的线性调频频率搜索数量，可以获得更高的时频集中度，然而，这会花费更高的计算资源。在所提出的 RLCT 中，通过采用单分量信号的局部搜索策略，极大地提高了搜索最佳线性调频速率或等效的时频平面上的旋转角度的能力。作为一个序列，即使具有重叠的瞬时频率，多分量信号的分辨率也通过采用自适应线性线性调频变换（ALCT）的思想而大大提高，其中具有高能量集中的分量被连续检测并从考虑中减去。采用两个关键指标来评估 TFA 方法的性能（准确性和分辨率）：总能量和能量比。后者被定义为以实际瞬时频率为中心的狭义频带内的能量相对于总能量的比例。验证示例表明，与短时傅里叶变换相比，基于 LCT 的方法在总能量方面显着提高了精度。 此外，在研究的 LCT 系列中，所提出的方法在能量比方面显着提高了分辨率，同时保持了算法的简单性。 RLCT 研究了强烈地震期间灯塔的地震响应，以揭示由于现有裂缝的张开和闭合而导致的频率下降和恢复。