Ju Wavelet – continuous wavelet transform and S transform for wave analysis

Abstract

This paper describes the Python package JuWavelet, which implements the continuous wavelet transform using the Morlet wavelet, which is a popular tool in the geosciences to analyse wave-like phenomena. It closes a gap in available software, which is typically focused on discrete transforms or lower dimensions than offered here. The code implements the transform in 1-D, 2-D, and 3-D. In particular, not only the analysis but also the synthesis from a (modified) decomposition is available. It also provides a consistent implementation for both the original continuous wavelet transform and the derivative and arguably superior S transform popular in atmospheric gravity wave analysis for all dimensions. This paper documents the mathematics behind the implementation and offers several examples to showcase the capabilities of the software including the code to generate the figures shown.