Geometric and Topological Methods for Significance Testing in Wavelet Analysis

Performs the geometric significance test on features in wavelet power and coherence spectra

The functions collectively calculate geometric and statistical properties of so-called pointwise significance patches, contiguous regions of pointwise significance in wavelet power and coherence spectra. The code is a modified version of the code written by A. Grinsted available at http://www.pol.ac.uk/home/research/waveletcoherence/ and that written by Eric K. W. Ng available at http://www.cityu.edu.hk/gcacic/wavelet/. In particular, the normalized areas of patches are computed and are use to assess the geometric significance of the patches relative to a null distribution, reducing the number of spurious results obtained from the pointwise test.
The testing procedure can be applied to wavelet power spectra obtained from the Paul, Morlet, and Dog wavelets and to patches at various pointwise significance levels. The number of holes in patches at a desired pointwise significance level can also be computed. A plotting routine is included to display the results of the geometric testing procedure.
Schulte, J. A., Duffy, C., and Najjar, R. G.: Geometric and topological approaches to significance testing in wavelet analysis, Nonlin. Processes Geophys., 22, 139-156, doi:10.5194/npg-22-139-2015, 201