Morse wavelets. Basic code to calculate the wavelet transform as well as the coherence analysis of several time series. Note that the phase estimate and uncertainty estimate is set for the scenario that the 1^st and 3^rd components only are of interest. The polarization estimate is valid in the general set-up.

See also my collaborator (Jonathan Lilly’s) excellent package - http://www.jmlilly.net/jmlsoft.html

The papers that go with this code are:

Olhede, S.C. and Walden, A.T. Generalized Morse wavelets. IEEE Trans. Signal Processing, 50, 2661-2670, 2002.

Olhede, S.C. and Walden, A.T. Polarization phase relationships via multiple Morse wavelets - Part I: Fundamentals. Proc. R. Soc. Lond. A., 459, 413-44, 2003.

Olhede, S.C. and Walden, A.T. Polarization phase relationships via multiple Morse wavelets - Part II: Data analysis. Proc. R. Soc. Lond. A., 459, 641-57, 2003.

Olhede, S.C. and Walden, A.T. Noise reduction in directional signals illustrated on quadrature Doppler ultrasound. IEEE Trans. on Biomedical Engineering, 50, 51-57, 2003.

Lilly J. and Olhede S. C. On the Design of Optimal Analytic Wavelets, Department of Statistical Science Reseach Report 289. Version available at http://arxiv.org/abs/0802.2377 Lilly J. and Olhede S. C. On the analytic wavelet transform. Statistics section technical report TR-07-02. Version available at: http://arxiv.org/abs/0711.3834