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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: firstname.lastname@example.org 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  Mallat, S. (2008). A wavelet tour of signal processing: The sparse way. Academic Press, 2008, 805.  Addison, P. S. (2002). The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance. IOP Publishing.  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.  Torrence, C. and Webster, P. J. (1999). Interdecadal changes in the ENSO-Monsoon system, Journal of Climate, 12(8), 2679-2690.  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.  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.