Getting started

PyCWT is a Python module for continuous wavelet spectral analysis. It includes a collection of routines for wavelet transform and statistical analysis via FFT algorithm. In addition, the module also includes cross-wavelet transforms, wavelet coherence tests and sample scripts. The code is based on Torrence and Compo (1998)[1]. Additional useful references are listed at the end of this page.

This module requires NumPy and SciPy. In addition, you also need matplotlib to run the samples.

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.

Installation

You can use PyPI to install this package.

>> pip install pycwt

Or, you can download the code and run the below line within the top level folder.

>> python setup.py install

Acknowledgements

We 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.

Authors

Sebastian Krieger, Nabil Freij, Alexey Brazhe, Christopher Torrence, Gilbert P. Compo and contributors.

Disclaimer

This module is based on routines provided by C. Torrence and G. P. 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 is released under a BSD-style open source license. Please read the license file for further information. This routine is provided as is without any express or implied warranties whatsoever.

References

[1]Torrence, C. and Compo, G. P.. A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society, American Meteorological Society, 1998, 79, 61-78. DOI.
[2]Torrence, C. and Webster, P. J.. Interdecadal changes in the ENSO-Monsoon system, Journal of Climate, 1999, 12(8), 2679-2690. DOI.
[3]Grinsted, A.; Moore, J. C. & Jevrejeva, S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, 2004, 11, 561-566. DOI.
[4]Mallat, S.. A wavelet tour of signal processing: The sparse way. Academic Press, 2008, 805.
[5]Addison, P. S. The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance. IOP Publishing, 2002. DOI.
[6]Liu, Y., Liang, X. S. and Weisberg, R. H. Rectification of the bias in the wavelet power spectrum. Journal of Atmospheric and Oceanic Technology, 2007, 24, 2093-2102. DOI.