A Signal Separation Method Based on Instantaneous Frequency Embedded Continuous Wavelet Transform and Short-Time Fourier Transform

Abstract

Modeling a non-stationary, multicomponent signal as a superposition of frequency components, each with a well-defined instantaneous frequency (IF), is crucial for extracting information, such as the underlying dynamics hidden within the signal. The synchrosqueezing transform (SST) has emerged as an alternative to empirical mode decomposition (EMD) for separating non-stationary signals. However, because the SST estimates the IFs of all frequency components based on a single phase transformation, its accuracy can be limited. To address this, SST variants based on the IF-embedded short-time Fourier transform (IFE-STFT) and the IF-embedded continuous wavelet transform (IFE-CWT) were developed.
More recently, a direct time-frequency method called the signal separation operation (SSO) was introduced for multicomponent signal separation. SSO bypasses the second step of the two-step SST method for component recovery and is based on variants of the STFT or CWT. In this paper, we propose a direct signal separation method by combining the SSO method with IFE-CWT and IFE-STFT, creating the IFE-CWT-based SSO (IWSSO) and the IFE-STFT-based SSO (IFSSO). Both IWSSO and IFSSO directly separate multicomponent signals without the squeezing operation inherent in SST. Our algorithms and techniques yield more accurate instantaneous frequency estimates and signal separation than conventional SSO or SST methods.