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ebrevdo / synchrosqueezing

The MATLAB Synchrosqueezing Toolbox
https://ebrevdo.github.io/synsq/
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Synchrosqueezing Toolbox v1.21 Authors: Eugene Brevdo, Gaurav Thakur

If you use this code in your research, please include the citations to the papers below.

Acknowledgements

Hau-tieng Wu and Ingrid Daubechies were instrumental in the creation of the underlying ideas behind the Synchrosqueezing transform code in this toolbox.

The file curve_ext.c was authored by Jianfeng Lu (now at Duke).

Introduction

This toolbox implements several time-frequency and time-scale analysis methods, as described in [1,2,3,4]. These include:

  1. Forward and inverse discretized Continuous Wavelet Transform (CWT).
  2. Forward and inverse CWT-based Synchrosqueezing (synsq_cwt) and STFT-based Synchrosqueezing (synsq_stft).
  3. Various plotting and curve extraction utilities to go with the above functions.
  4. A GUI (the Synchrosqueezing GUI) for analysis, filtering, denoising, and signal extraction. This allows for simple, fast, initial analysis via Synchrosqueezing.

Installation

  1. You will need the MATLAB Image Processing toolbox for some of the GUI filtering tools used by gsynsq (see basic command reference below).

  2. Put the contents of the synchrosqueezing toolbox somewhere (say, $HOME/matlab/).

  3. Add the new directories to your path permanently; e.g., add the following to your startup.m: addpath ~/matlab/synchrosqueezing; addpath ~/matlab/util;

Basic command reference

gsynsq: The synchrosqueezing GUI. Run it without any parameters and use the menu items and keyboard shortcuts to analyze signals. To import time/signal vectors from your workspace, use file->import (control+I). To export analysis output when done, use file->export (control+E). This GUI calls, and provides examples for using, many of the functions described below.

cwt_fw, cwt_iw: continuous wavelet forward/inverse transform

synsq_cwt_fw, synsq_cwt_iw: CWT Synchrosqueezing forward/inverse transform.

synsq_stft_fw, synsq_stft_iw: STFT Synchrosqueezing forward/inverse transform.

est_riskshrink_thresh: RiskShrink threshold estimator for denoising signals.

tplot, tplot_power: plotting of output of cwt_fw, stft_fw, synsq_cwt, synsq_stft

curveext: different types of curve extraction from output of synsq_cwt or synsq_stft plot_ext_curves: associated plotting functions

synsq_filter_pass: frequency-region filtering in synchrosqueezing domain.

examples: several example scripts illustrating how the above functions work

References

  1. Mallat, S., Wavelet Tour of Signal Processing 3rd ed.

  2. I. Daubechies, J. Lu, H.T. Wu, "Synchrosqueezed Wavelet Transforms: an empricial mode decomposition-like tool", Applied and Computational Harmonic Analysis 30(2):243-261, 2011.

  3. G. Thakur, E. Brevdo, N.-S. Fučkar, and H.-T. Wu, "The Synchrosqueezing algorithm for time-varying spectral analysis: robustness properties and new paleoclimate applications", Signal Processing 93:1079-1094, 2013.

  4. G. Thakur and H.-T. Wu, "Synchrosqueezing-based Recovery of Instantaneous Frequency from Nonuniform Samples", SIAM Journal on Mathematical Analysis, 43(5):2078-2095, 2011.