Instantaneous frequency estimation based on synchrosqueezing wavelet transform

The instantaneous frequency-embedded continuous wavelet transform (IFE-CWT) is introduced and its properties are studied.Based on IFE-CWT, the instantaneous frequency-embedded synchrosqueezing transform (IFE-SST) is introduced.IFE-SST can preserve the IF of a monocomponent signal. To estimate IF of a component of a multicomponent signal, IFE-SST uses a reference IF function associated with that component.The IFE-SST-based multicomponent signal separation algorithm is proposed. The experimental results also show that IFE-SST works well in the noise environment. Recently, the synchrosqueezing transform (SST) was developed as an alternative to the empirical mode decomposition scheme to separate a non-stationary signal with time-varying amplitudes and instantaneous frequencies (IFs) into a superposition of frequency components that each have well-defined IFs. The continuous wavelet transform (CWT)-based SST sharpens the time-frequency representation of a non-stationary signal by assigning the scale variable of the signals CWT to the frequency variable by a reference IF function. Since the SST method is applied to estimate the IFs of all frequency components of a signal based on one single reference IF function, it may yield not very accurate results. In this paper we introduce the instantaneous frequency-embedded synchrosqueezing wavelet transform (IFE-SST). IFE-SST uses a rough estimation of the IF of a targeted component to produce accurate IF estimation. The reference IF function of IFE-SST is associated with the targeted component. Our numerical experiments show that IFE-SST outperforms the CWT-based SST in IF estimation and separation of multicomponent signals.