Analysis of adaptive short-time Fourier transform-based synchrosqueezing transform

Recently the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method for instantaneous frequency estimation and component separation 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. Very recently the FSST with a time-varying parameter, called the adaptive FSST, was introduced. The simulation experiments show that the adaptive FSST is very promising in instantaneous frequency estimation of the component of a multicomponent signal, and in accurate component recovery. However the theoretical analysis of the adaptive FSST has not been carried out. In this paper, we study the theoretical analysis of the adaptive FSST and obtain the error bounds for the instantaneous frequency estimation and component recovery with the adaptive FSST and the 2nd-order adaptive FSST.

[1]  Sylvain Meignen,et al.  The fourier-based synchrosqueezing transform , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[2]  Yi Wang,et al.  ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform , 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  Charles K. Chui,et al.  Signal decomposition and analysis via extraction of frequencies , 2016 .

[4]  Sylvain Meignen,et al.  The second-order wavelet synchrosqueezing transform , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[5]  Patrick Flandrin,et al.  Improving the readability of time-frequency and time-scale representations by the reassignment method , 1995, IEEE Trans. Signal Process..

[6]  Lin Li,et al.  An empirical signal separation algorithm for multicomponent signals based on linear time-frequency analysis , 2019, Mechanical Systems and Signal Processing.

[7]  Sylvain Meignen,et al.  Second-Order Synchrosqueezing Transform or Invertible Reassignment? Towards Ideal Time-Frequency Representations , 2015, IEEE Transactions on Signal Processing.

[8]  Qingtang Jiang,et al.  Adaptive Short-time Fourier Transform and Synchrosqueezing Transform for Non-stationary Signal Separation , 2018, Signal Process..

[9]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[10]  Sylvain Meignen,et al.  On Demodulation, Ridge Detection, and Synchrosqueezing for Multicomponent Signals , 2017, IEEE Transactions on Signal Processing.

[11]  Hau-Tieng Wu,et al.  The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications , 2011, Signal Process..

[12]  Hau-Tieng Wu,et al.  Synchrosqueezing-Based Recovery of Instantaneous Frequency from Nonuniform Samples , 2010, SIAM J. Math. Anal..

[13]  Haizhao Yang,et al.  Synchrosqueezed wave packet transforms and diffeomorphism based spectral analysis for 1D general mode decompositions , 2013, 1311.4655.

[14]  ThakurGaurav,et al.  The Synchrosqueezing algorithm for time-varying spectral analysis , 2013 .

[15]  Haizhao Yang.  Statistical analysis of synchrosqueezed transforms , 2014, Applied and Computational Harmonic Analysis.

[16]  Hau-Tieng Wu,et al.  Entropy-based time-varying window width selection for nonlinear-type time–frequency analysis , 2015, International Journal of Data Science and Analytics.

[17]  Charles K. Chui,et al.  Real-time dynamics acquisition from irregular samples -- with application to anesthesia evaluation , 2014, 1406.1276.

[18]  Shibin Wang,et al.  Matching synchrosqueezing transform: A useful tool for characterizing signals with fast varying instantaneous frequency and application to machine fault diagnosis , 2018 .

[19]  Gaigai Cai,et al.  Matching Demodulation Transform and SynchroSqueezing in Time-Frequency Analysis , 2014, IEEE Transactions on Signal Processing.

[20]  Bruce W. Suter,et al.  Instantaneous frequency estimation based on synchrosqueezing wavelet transform , 2017, Signal Process..

[21]  Chuan Li,et al.  A generalized synchrosqueezing transform for enhancing signal time-frequency representation , 2012, Signal Process..

[22]  Sylvain Meignen,et al.  High-Order Synchrosqueezing Transform for Multicomponent Signals Analysis—With an Application to Gravitational-Wave Signal , 2017, IEEE Transactions on Signal Processing.

[23]  I. Daubechies,et al.  Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool , 2011 .

[24]  T. Oberlin,et al.  Theoretical analysis of the second-order synchrosqueezing transform , 2016, Applied and Computational Harmonic Analysis.

[25]  Peter V. E. McClintock,et al.  Linear and synchrosqueezed time-frequency representations revisited: Overview, standards of use, resolution, reconstruction, concentration, and algorithms , 2015, Digit. Signal Process..

[26]  Naoki Saito,et al.  Adaptive synchrosqueezing based on a quilted short-time Fourier transform , 2017, Optical Engineering + Applications.

[27]  Charles K. Chui,et al.  Signal analysis via instantaneous frequency estimation of signal components , 2015 .

[28]  IatsenkoDmytro,et al.  Linear and synchrosqueezed time-frequency representations revisited , 2015 .

[29]  Qingtang Jiang,et al.  Adaptive synchrosqueezing transform with a time-varying parameter for non-stationary signal separation , 2018, Applied and Computational Harmonic Analysis.