Signal Separation Operator Based on Wavelet Transform for Non-Stationary Signal Decomposition

Abstract

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.

Keywords

• non-stationary signal separation
• instantaneous frequency
• continuous wavelet transform