Signal Separation Based on Adaptive Continuous Wavelet Transform and Analysis

Abstract

In nature and engineering world, the measured signals are usually affected by multiple complicated factors and they appear as multicomponent non-stationary modes. In many situations we need to separate these signals to a finite number of mono-components to represent the intrinsic modes and underlying dynamics implicated in the source signals. Recently the synchrosqueezing transform (SST) was developed as an empirical mode decomposition (EMD)-like tool to enhance the time-frequency resolution and energy concentration of a multicomponent non-stationary signal and provides more accurate component recovery. To recover individual components, the SST method consists of two steps. First the instantaneous frequency (IF) of a component is estimated from the SST plane. Secondly, after IF is recovered, the associated component is computed by a definite integral along the estimated IF curve on the SST plane. The reconstruction accuracy for a component depends heavily on the accuracy of the IFs estimation carried out in the first step.More recently, a direct method of the time-frequency approach, called signal separation operation (SSO), was introduced for multicomponent signal separation. While both SST and SSO are mathematically rigorous on IF estimation, SSO avoids the second step of the two-step SST method in component recovery (mode retrieval).The SSO method is based the short-time Fourier transform. In this paper we propose a direct method of signal separation based on the adaptive continuous wavelet transform (CWT). We introduce two models of the adaptive CWT-based approach for signal separation: the sinusoidal signal-based model and the linear chirp-based model, which are derived respectively from