TOOLBOX of ASST_v1



1. This is a collection of Matlab routines developed for the adaptive CWT, adaptive SST and 2nd-order adaptive SST described in [1].


2. List of functions included:


MAIN ROUTINES:

MAIN - This is an example for the two-component LFM signal

RENYI_ENTROPY - Find the time-varying sigma by Renyi entropy

CWT_MC_TI - Computes the CWT Ws for a fixed time ti

BOUNDARY_CWT - Calculate the boundaries of multicomponent on the CWT plane;

IMAGESQ - Displays time-frequency result of the Synchrosqueezing transform

CWT_SST_MC_TI - Computes the CWT Ws, the phase transform of CWT Rs, and the  synchrosqueezing transform SST Ts of the signal s.

CWT_SST_MC - Computes the CWT Ws, the phase transform of CWT Rs, and the  synchrosqueezing transform SST Ts of the signal s.

RENYI_ENTROPY_GLOBAL - Computes concentration of a time-frquency distribution.

CWT_2ND_ORDER_SST_TV - Computes the ADAPTIVE Continuous Wavelet transform: Ws, the ADAPTIVE 1st-order time-varying synchrosqueezing transform: Ts1_vt; the ADAPTIVE 2nd-order time-varying synchrosqueezing transform: Ts2_vt   and the phase transform w2nd.


3. ACKNOWNLEGEMENT: We thank Duong Hung PHAM and Sylvain Meignen for their toolbox FSSTn-master,  thank  E. Brevdo and G. Thakur for their Synchrosqueezing Toolbox v1.21.


4. REFERENCES
[1] Lin Li, Haiyan Cai, and Qingtang Jiang, "Adaptive synchrosqueezing transform with a time-varying parameter for non-stationary signal separation," preprint, 2018, arXiv:1812.11364.

[2] Thakur, Gaurav, Eugene Brevdo, Neven S. Fuckar, and Hau-Tieng Wu. "The synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications," Signal Processing 93, no. 5 (2013): 1079-1094. 

[3] T. Oberlin,  S. Meignen, and V. Perrier. "Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time-frequency representations," IEEE Transactions on Signal Processing 63, no. 5 (2015): 1335-1344.

[4] E. Brevdo and H.-T. Wu, The Synchrosqueezing Toolbox, 2011 https://web.math.princeton.edu/~ebrevdo/synsq/.

[5] Lin Li, Haiyan Cai, Hongxia Han, Qingtang Jiang, and Hongbing Ji, "Adaptive short-time Fourier transform and synchrosqueezing transform for non-stationary signal separation," preprint, 2018, arXiv:1812.11292.

[6] Haiyan Cai, Qingtang Jiang, Lin Li, and Bruce W. Suter, "Analysis of adaptive short-time Fourier transform-based synchrosqueezing," preprint, 2018, arXiv:1812.11033.


5. Copy ASST_v1 is copyright reserved. For further information, please contact Lin Li at  lilin@xidian.edu.cn or Qingtang Jiang at jiangq@umsl.edu.

May 2018 


This toolbox can not be used for commercialization without the authorization of its author(s). If you use this toolbox for research, please must cite the following paper:
[1] Lin Li, Haiyan Cai and Qingtang Jiang, "Adaptive synchrosqueezing transform with a time-varying parameter for non-stationary signal separation," preprint, 2018, arXiv:1812.11364.