Instantaneous frequency-embedded synchrosqueezing transform for signal separation
Suter, Bruce W
MetadataShow full item record
Jiang Q, Prater-Bennette A, Suter BW and Zeyani A (2022) Instantaneous Frequency-Embedded Synchrosqueezing Transform for Signal Separation. Front. Appl. Math. Stat. 8:830530. doi: 10.3389/fams.2022.830530
The synchrosqueezing transform (SST) and its variants have been developed recently as an alternative to the empirical mode decomposition scheme to model a non-stationary signal as a superposition of amplitude- and frequency-modulated Fourier-like oscillatory modes. In particular, SST performs very well in estimating instantaneous frequencies (IFs) and separating the components of non-stationary multicomponent signals with slowly changing frequencies. However its performance is not desirable for signals having fast-changing frequencies. Two approaches have been proposed for this issue. One is to use the 2nd-order or high-order SST, and the other is to apply the instantaneous frequency-embedded SST (IFE-SST). For the SST or high order SST approach, one single phase transformation is applied to estimate the IFs of all components of a signal, which may yield not very accurate results in IF estimation and component recovery. IFE-SST uses an estimation of the IF of a targeted component to produce accurate IF estimation. The phase transformation of IFE-SST is associated with the targeted component. Hence the IFE-SST has certain advantages over SST in IF estimation and signal separation. In this article, we provide theoretical study on the instantaneous frequency-embedded short-time Fourier transform (IFE-STFT) and the associated SST, called IFE-FSST. We establish reconstructing properties of IFE-STFT with integrals involving the frequency variable only and provide reconstruction formula for individual components. We also consider the 2nd-order IFE-FSST.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.