Han Ningning, Pei Yongzhen, Song Zhanjie
School of Mathematical Sciences, Tiangong University, Tianjin 300387, China.
Geogia Tech Shenzhen Institute, Tianjin University, Shenzhen 518055, China.
Sensors (Basel). 2024 Sep 18;24(18):6026. doi: 10.3390/s24186026.
This paper develops a new frame for non-stationary signal separation, which is a combination of wavelet transform, clustering strategy and local maximum approximation. We provide a rigorous mathematical theoretical analysis and prove that the proposed algorithm can estimate instantaneous frequencies and sub-signal modes from a blind source signal. The error bounds for instantaneous frequency estimation and sub-signal recovery are provided. Numerical experiments on synthetic and real data demonstrate the effectiveness and efficiency of the proposed algorithm. Our method based on wavelet transform can be extended to other time-frequency transforms, which provides a new perspective of time-frequency analysis tools in solving the non-stationary signal separation problem.
本文提出了一种用于非平稳信号分离的新框架，它是小波变换、聚类策略和局部最大值逼近的结合。我们提供了严格的数学理论分析，并证明了所提出的算法可以从盲源信号中估计瞬时频率和子信号模式。给出了瞬时频率估计和子信号恢复的误差界。对合成数据和真实数据的数值实验证明了所提算法的有效性和高效性。我们基于小波变换的方法可以扩展到其他时频变换，这为解决非平稳信号分离问题的时频分析工具提供了一个新的视角。
