A Signal Separation Method Based on Adaptive Continuous Wavelet Transform and its Analysis
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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 (mode retrieval). 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. More recently, a direct method of the time-frequency approach, called signal separation operation (SSO), was introduced for multicomponent signal separation. SSO avoids the second step of the two-step SST method in component recovery. 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 sinusoidal signal approximation and the linear chirp approximation at any local time. A more accurate component recovery formula is derived from linear chirp local approximation. We present the theoretical analysis of our approach. For each model, we establish the error bounds for IF estimation and component recovery.
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