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Continuous wavelet transform module for Python. Includes a collection of routines for wavelet transform and statistical analysis via FFT algorithm. This module references to the numpy, scipy and pylab Python packages.
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Continuous wavelet transform module for Python. Includes a collection of
routines for wavelet transform and statistical analysis via FFT algorithm.
Most recently cross-wavelet tranforms, wavelet coherence tests and plotting
functions were added to the module.
This module references to the numpy, scipy, pylab and maybe other Python
packages.
The sample scripts (sample.py, sample_xwt.py) illustrate the use of the
wavelet and inverse wavelet transforms, cross-wavelet transform and wavelet
transform coherence. Results are plotted in figures similar to the sample
images.
DISCLAIMER
This module is based on routines provided by C. Torrence and G. P. Compo
Compo available at http://paos.colorado.edu/research/wavelets/, on
routines provided by A. Grinsted, J. Moore and S. Jevrejeva available at
http://noc.ac.uk/using-science/crosswavelet-wavelet-coherence, and
on routines provided by A. Brazhe available at
http://cell.biophys.msu.ru/static/swan/.
This software may be used, copied, or redistributed as long as it
is not sold and this copyright notice is reproduced on each copy
made. This routine is provided as is without any express or implied
warranties whatsoever.
INSTALLATION
Copy all the contents into a location included in the Python search
path. On Linux distribution one such option is
~/.local/lib/python2.x/site-packages/kPyWavelet
COMMENTS
There is an errata page at the wavelet website maintaned at the Program
in Atmospheric and Oceanic Sciences, University of Colorado, Boulder,
Colorado, wich was (is) accessible throught the link
http://paos.colorado.edu/research/wavelets/errata.html
A Practical Guide to Wavelet Analysis
Christopher Torrence and Gilbert P. Compo
Errata
~~~~~~
- Figure 3: N/(2 sigma^2) should just be N/sigma^2.
- Equation (17), left-hand side: Factor of 1/2 should be removed.
- Table 1, DOG, Psi-hat (third column, bottom row): Should be a minus sign
in front of the equation.
- Sec 3f, last paragraph: Plugging N=506, dt=1/4 yr, s0=2dt, and dj=0.125
into Eqn (10) actually gives J=64, not J=56 as stated in the text.
However, in Figure 1b, the scales are only plotted out to J=56 since the
power is so low at larger scales.
Additional information
~~~~~~~~~~~~~~~~~~~~~~
Table 3: Cross-wavelet significance levels, from Eqn.(30)-(31).
(DOF = degrees of freedom)
Significance level Real wavelet (1 DOF) Complex wavelet (2 DOF)
0.10 1.595 3.214
0.05 2.182 3.999
0.01 3.604 5.767
ACKNOWLEDGEMENTS
I would like to thank Christopher Torrence, Gilbert P. Compo, Aslak
Grinsted, John Moore, Svetlana Jevrejevaand and Alexey Brazhe for their
code and also Jack Ireland and Renaud Dussurget for their attentive eyes,
feedback and debugging.
AUTHOR
Sebastian Krieger
email: sebastian@nublia.com
REVISION
4 (2013-03-06 19:37 -3000)
3 (2011-04-30 19:48 -3000)
2 (2011-04-28 17:57 -0300)
1 (2010-12-24 21:59 -0300)
REFERENCES
[1] Mallat, S. (2008). A wavelet tour of signal processing: The
sparse way. Academic Press, 2008, 805.
[2] Addison, P. S. (2002). The illustrated wavelet transform
handbook: introductory theory and applications in science,
engineering, medicine and finance. IOP Publishing.
[3] Torrence, C. and Compo, G. P. (1998). A Practical Guide to
Wavelet Analysis. Bulletin of the American Meteorological
Society, American Meteorological Society, 1998, 79, 61-78.
[4] Torrence, C. and Webster, P. J. (1999). Interdecadal changes in
the ENSO-Monsoon system, Journal of Climate, 12(8), 2679-2690.
[5] Grinsted, A.; Moore, J. C. & Jevrejeva, S. (2004). Application
of the cross wavelet transform and wavelet coherence to
geophysical time series. Nonlinear Processes in Geophysics, 11,
561-566.
[6] Liu, Y.; Liang, X. S. and Weisberg, R. H. (2007). Rectification
of the bias in the wavelet power spectrum. Journal of
Atmospheric and Oceanic Technology, 24(12), 2093-2102.
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Continuous wavelet transform module for Python. Includes a collection of routines for wavelet transform and statistical analysis via FFT algorithm. This module references to the numpy, scipy and pylab Python packages.
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