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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README

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.