In existing window time-frequency analysis methods, its resolution is commonly limited by the uncertainty principle. The time resolution and the frequency resolution restrict each other and cannot reach the maximum at the same time. For this reason, we employ the secondary processing technology of the time-frequency spectrum to enhance the time resolution of the S-transform (ST). By performing multiband filtering with a filter bank, the ST is capable of receiving the signal under different frequencies and its time-frequency coefficient. The window size is different, that is, the low-frequency time window is long, resulting in low time resolution and high-frequency resolution. The high-frequency time window is short, which makes the time resolution high and the frequency resolution low; however, the window size for the time component of each frequency is fixed. Based on the above idea, we perform “de-window” processing for each frequency component signal. We assume that the time-frequency spectrum is sparse without “windowing,” so the window effect can be removed by sparse inversion. Based on the alternating direction method of multipliers (ADMM), we use the nonnegative penalty terms and sparse terms for the joint constraints to solve the optimization problem, and obtain the sparse time-frequency spectrum to enhance the time resolution. This time sparse ST (TSST) obtained by the proposed method is suitable for improving the ability of thin-layer identification and also for the analysis of transient signals.

中文翻译：

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时间稀疏 S 变换 (TSST) 及其应用


现有的窗时频分析方法中，其分辨率普遍受到不确定性原理的限制。时间分辨率和频率分辨率相互制约，不能同时达到最大值。为此，我们采用时频谱二次处理技术来提高S变换（ST）的时间分辨率。通过滤波器组进行多频段滤波，ST能够接收不同频率下的信号及其时频系数。窗口大小不同，即低频时间窗口长，导致时间分辨率低，频率分辨率高。高频时间窗短，时间分辨率高，频率分辨率低；然而，每个频率的时间分量的窗口大小是固定的。基于上述思想，我们对每个频率分量信号进行“去窗”处理。我们假设时频谱是稀疏的，没有“加窗”，因此可以通过稀疏反演来消除窗口效应。基于乘子交替方向法（ADMM），采用非负惩罚项和稀疏项作为联合约束来求解优化问题，获得稀疏时频谱以提高时间分辨率。本次提出的方法得到的稀疏ST（TSST）适用于提高薄层识别能力，也适用于瞬态信号的分析。