EMD: This toolbox aims at decomposing any nonstationary signal into IMFs. The decomposition procedure is based on the sifting process. X is a real vector. The result is stacked in a matrix IMF containing one IMF per row, the
last one being the residue.
Reference:
G. Rilling, P. Flandrin, P. Gonçalves,
"On empirical mode decomposition and its algorithms",
IEEE-EURASIP workshop on nonlinear signal and image processing 3, 8-11
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HHT (Wu-Huang): This toolbox aims at decomposing any non-stationary signal in IMFs and to provide a spectral analysis of each mode.
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CEEMDAN: This toolbox allows us to perform an ensemble empirical mode decomposition (EEMD). The key idea on the EEMD relies on averaging the modes obtained by EMD applied to several realizations of Gaussian white noise added to the original signal. The resulting decomposition solves the EMD mode mixing problem, however it introduces new ones.
In the method here proposed, a particular noise is added at each stage of the decomposition and a unique residue is computed to obtain each mode. The resulting decomposition is complete, with a numerically negligible error. Two examples are presented: a discrete Dirac delta function and an electrocardiogram signal. The results show that, compared with
EEMD, the new method here presented also provides a better spectral separation of the modes and a lesser number of sifting iterations is needed, reducing the computational cost.
Reference:
M.E.Torres, M.A. Colominas, G. Schlotthauer, P. Flandrin,
"A complete Ensemble Empirical Mode decomposition with adaptive noise,"
IEEE Int. Conf. on Acoust., Speech and Signal Proc. ICASSP-11, pp. 4144-4147, Prague (CZ)
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EMD 2D : This toolbox aims at decomposing any non-stationary image in IMFs. This toolbox has been created by Christophe Damerval.
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Bidemensional EMD : This toolbox aims at decomposing any non-stationary image in IMFs. This toolbox is associated to the work by J.C. Nunes et al., "Image analysis by bidimensional empirical mode decomposition", Image and Vision Computing Journal (21), No. 12, pp. 1019-1026, 2003.
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HHT : This submission is a realization of the Hilbert-Huang transform (HHT). It has been developed by Alan Tan.
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Multivariate (Mandic): Empirical Mode Decomposition, Multivariate EMD, Multivariate Synchrosqueezing, Matlab code and data. It has been developed by Danilo P. Mandic.
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On-line: Li-aung "Lewis" Yip proposes a real-time (online) implementation of the Empirical Mode Decomposition. The original application was an extension of Chappell and Payne’s system for detecting gas emboli using Doppler ultrasound.
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Scilab toolbox for Empirical Mode Decomposition: Using the EMD method, any complicated data set can be decomposed into a finite
and often small number of components, which is a collection of intrinsic mode
functions (IMF). An IMF represents a generally simple oscillatory mode as a
counterpart to the simple harmonic function. By definition, an IMF is any
function with the same number of extrema and zero crossings, with its envelopes
being symmetric with respect to zero. The definition of an IMF guarantees a
well-behaved Hilbert transform of the IMF. This decomposition method operating
in the time domain is adaptive and highly efficient. Since the decomposition is
based on the local characteristic time scale of the data, it can be applied to
nonlinear and nonstationary processes.
Toolbox developed by Gabriel Rilling.
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Mathematica: Here a more or less straightforward translation of Alan Tan's MATLAB code to Mathematica code.
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Image EMD: Some implementations of the EMD in two dimensions generates a residue with many extrema points. In the associated papers the authors present an improved method that can decompose the image into a number of IMFs and a residue with none, or with only a few extrema points. This method makes it possible to use the EMD for image processing. They introduce the concept of empiquency, short for empirical mode frequency, to describe the signal oscillations when traditional frequency concept is not applicable in this work. They also discuss the selection of significant extrema points as a tool for noise reduction.
Toolbox developed by Anna Linderhed.
Reference:
A. Linderhed "Image Emprirical Mode Decomposition: A New Tool for Image Processing", Advances in Adaptive Data Analysis (AADA), vol.1, No. 2, 2009.
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EMD-DAMF : In this study, a Multifractal Formalism based on the Empirical Mode Decomposition is proposed. Scaling exponents are estimated from statistical moments computed over a discrete set of multiresolution parameters, namely, the dominant amplitude coefficients, which are selected among the local maxima observed across the set of envelopes of the Intrinsic Mode Functions. Analyses of synthetic fractal and multifractal processes demonstrate that the proposed technique is capable of overcoming the negative moment divergence problem, and is competitive with other multifractal formalisms.
Reference:
Guilherme S. Welter and Paulo A. A. Esquef, "Multifractal analysis based on amplitude extrema of intrinsic mode functions", Phys. Rev. E 87, 032916, March 2013.
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Recursive Time-frequency assignment : A fast algorithm for creating time-frequency representations based on a special case of the short-time Fourier transform (STFT). The algorithm is extended with the method known as time-frequency reassignment. This approach makes time-frequency reassignment well suited for real-time implementations.
This toolbox is associated to the work by G.K. Nielsen, "Recursive Time-frequency assignment", IEEE Trans. Signal Proc. (57), No. 8, pp. 3283-3287, 2009.
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Basic: The Time-Frequency Toolbox (TFTB) is a collection of about 100 scripts for GNU Octave and Matlab (R) developed for the analysis of non-stationary signals using time-frequency distributions. It is primary intended for researchers, engineers and students with some basic knowledge in signal processing.
The toolbox contains numerous algorithms which implements various kind of time-frequency analysis with a special emphasis on quadratic energy distributions of the Cohen and affine classes, along with their version enhanced by the reassignment method. The toolbox also includes signal generation procedures, processing/post-processing routines (with display utilities) and a number of demonstrations.
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Fitz: Webpage and Matlab code by Kelly Fitz.
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Multitaper: A method is proposed for obtaining time-frequency distributions of chirp signals embedded in nonstationary
noise, with the twofold objective of a sharp localization for the chirp components and a reduced level of statistical
fluctuations for the noise. The technique consists in combining time-frequency reassignment with multitapering, and
two variations are proposed. The first one, primarily aimed at nonstationary spectrum estimation, is based on sums
of estimates with different tapers, whereas the second one makes use of differences between the same estimates
for a sake of chirp enhancement. The principle of the technique is outlined, its implementation based on Hermite
functions is justified and discussed, and some examples are provided for supporting the efficiency of the approach,
both qualitatively and quantitatively.
Reference:
J. Xiao and P. Flandrin, "Multitaper time-frequency reassignment for nonstationary spectrum estimation and chirp enhancement," IEEE Trans. on Sig. Proc., vol. 55, no. 6, pp.2851--2860, June 2007.
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Recursive: A fast algorithm for creating time-frequency representations based on a special case of the short-time Fourier transform (STFT) is presented. The algorithm is extended with the method known as time-frequency reassignment. This approach makes time-frequency reassignment well suited for real-time implementations.
Reference:
G.K. Nielsen, "Recursive Time-Frequency Reassignment ," IEEE Trans. on Sig. Proc., vol. 57, no. 8, pp.3283--3287, April 2009.
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Gardner: Auditory neurons preserve exquisite temporal information about sound features, but we do not know how the brain uses this information to process the rapidly changing sounds of the natural world. Simple arguments for effective use of temporal information led us to consider the reassignment class of time-frequency representations as a model of auditory processing. Reassigned time-frequency representations can track isolated simple signals with accuracy unlimited by the time-frequency uncertainty principle, but lack of a general theory has hampered their application to complex sounds. We describe the reassigned representations for white noise and show that even spectrally dense signals produce sparse reassignments: the representation collapses onto a thin set of lines arranged in a froth-like pattern. Preserving phase information allows reconstruction of the original signal. We define a notion of “consensus,” based on stability of reassignment to time-scale changes, which produces sharp spectral estimates for a wide class of complex mixed signals. As the only currently known class of time-frequency representations that is always “in focus” this methodology has general utility in signal analysis. It may also help explain the remarkable acuity of auditory perception. Many details of complex sounds that are virtually undetectable in standard sonograms are readily perceptible and visible in reassignment.
Reference:
T.J. Gardner and M.O. Magnasco, "Sparse time-frequency representations," Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 16, pp:6094–6099, 2006.
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Recursive version of the
Levenberg-Marquardt reassigned spectrogram : Matlab toolbox for
recursive Levenberg-Marquardt reassignment and synchrosqueezing. Toolbox
developed by D. Fourer. More information available on his webpage.
Reference:
D. Fourer, F. Auger and P. Flandrin. Recursive versions of the
Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed
STFT. Proc. ICASSP 2016. Mar. 2016. Shanghai, China.
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Segtool: Matlab toolbox for synchrosqueezing. Toolbox developed by T. Oberlin.
Reference:
S. Meignen, T. Oberlin and S. McLaughlin, "A new algorithm for multicomponent signal analysis based on SynchroSqueezing: With an application to signal sampling and denoising", IEEE Transactions on Signal Processing, Vol. 60(11), pp. 5787--5798, 2012.
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Princeton: Matlab toolbox for synchrosqueezing. Toolbox developed by E. Brevdo.
References:
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," Submitted, 2012.
I. Daubechies, J. Lu, and H.-T. Wu, "Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool," Applied and Computational Harmonic Analysis, 2010.
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Youtube tutorial: Calculation of Synchrosqueezed WFT and WT in MatLab.
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Recursive version of the
Levenberg-Marquardt of the synchrosqueezed
STFT : Matlab toolbox for
recursive Levenberg-Marquardt reassignment and synchrosqueezing. Toolbox
developed by D. Fourer. More information available on his webpage.
Reference:
D. Fourer, F. Auger and P. Flandrin. Recursive versions of the
Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed
STFT. Proc. ICASSP 2016. Mar. 2016. Shanghai, China.
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Combo: The following package and source code is based on F. Auger, P. Flandrin, Y-T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, H-T. Wu, "An Overview of Time-Frequency Reassignment and Synchrosqueezing".
Reference:
F. Auger, P. Flandrin, Y.-T. Lin, S. McLaughlin, S. Meignen, T. Oberlin and H.-T. Wu, "Time-Frequency Reassignment and Synchrosqueezing: An Overview", IEEE Signal Processing Magazine, vol. 30, nu. 6, pp. 32--41, 2013
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LTFAT: The Large Time/Frequency Analysis Toolbox is a Matlab/Octave/C toolbox for doing time/frequency and wavelet analysis. It is inteded as both an educational and a computational tool.
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