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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