TY - JOUR
T1 - A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation
AU - Lu , Jian
AU - Alzahrani , Jawaher H.
AU - Jiang , Qingtang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 624
EP - 649
PY - 2021
DA - 2021/06
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0077
UR - https://global-sci.org/intro/article_detail/nmtma/19192.html
KW - Short-time Fourier transform, second-order synchrosqueezing transform, phase
transformation, instantaneous frequency estimation, multicomponent signal separation.
AB - <p style="text-align: justify;">To model a non-stationary signal as a superposition of amplitude and
frequency-modulated Fourier-like oscillatory modes is important to extract information, such as the underlying dynamics, hidden in the signal. Recently, the synchrosqueezed wavelet transform (SST) and its variants have been developed to estimate instantaneous frequencies and separate the components of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST for short)
reassigns the frequency variable to sharpen the time-frequency representation and to
separate the components of a multicomponent non-stationary signal. However, FSST
works well only with multicomponent signals having slowly changing frequencies.
To deal with multicomponent signals having fast-changing frequencies, the second-order FSST (FSST2 for short) was proposed. The key point for FSST2 is to construct
a phase transformation of a signal which is the instantaneous frequency when the
signal is a linear chirp. In this paper we consider a phase transformation for FSST2
which has a simpler expression than that used in the literature. In the study the
theoretical analysis of FSST2 with this phase transformation, we observe that the
proof for the error bounds for the instantaneous frequency estimation and component recovery is simpler than that with the conventional phase transformation. We
also provide some experimental results which show that this FSST2 performs well
in non-stationary multicomponent signal separation.</p>