Functions for time continuous wavelet transform and bivariate wavelet analysis, implemented in Julia.
Description: A collection of simple functions to perform time continunuous wavelet transform (CWT) and bivariate wavelet analysis, including wavelet cross spectrum (WCS), scale-time averaging, amplitude-phase separation, wavelet coherence (WCO), significance testing, and plotting. All functions assume that input data contain time series of real (or integer) numbers, given at a constant sampling rate (a function to handle missing data and to interpolate irregular data is provided).
Further included are some small function for fft-transform of real valued signals, plus (naive) power spectrum and Hilbert transform.
The code for the wavelet transform (in the function src/wavelet.jl) essentially is a straightforward Julia translation of the 1d Wavelet transform from Torrence and Compo (see original copyright below).
The other functions are extensions for bivariate wavelet and phase analysis.
This repository does not aspire to be exhaustive.
The repository just contains a colloection of functions that I developed in the context of a recent paper and want to make open for public use:
Blasius et al. (2019) Long-term cyclic persistence in an experimental predator-prey system.
Nature. DOI
Please acknowledge the use of this software by citing the above publication.
Data: The folder data contains some sample time series, e.g. the El Nino time series, the Canadian hare-lynx cycle, and the predator-prey time series from the reference Blasius et al (2019)
Code: The folder src contains the main algorithms, the folder examples contains some worked-out examples, demonstrating how to apply the algorithms and visualize the results.
Original copyright for the wavelet transform code:
Copyright (C) 1995-2004, Christopher Torrence and Gilbert P. Compo
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.
Notice: Please acknowledge the use of the above software in any publications: Wavelet software was provided by C. Torrence and G. Compo, and is available at URL: http://paos.colorado.edu/research/wavelets/.
Reference: Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78.
Please send a copy of such publications to either C. Torrence or G. Compo: Dr. Christopher Torrence Dr. Gilbert P. Compo Research Systems, Inc. Climate Diagnostics Center 4990 Pearl East Circle 325 Broadway R/CDC1 Boulder, CO 80301, USA Boulder, CO 80305-3328, USA E-mail: chris[AT]rsinc[DOT]com E-mail: compo[AT]colorado[DOT]edu