Data-driven wavelets
README for Data-Driven Wavelet Decomposition (DDWD)
This distribution contains the code needed to create data-driven wavelets, as described in "Discovering multiscale and self-similar structure with data-driven wavelets," by D. Floryan and M. D. Graham, PNAS, 2021.
This distribution contains five primary MATLAB functions:
- waveletOpt.m: calculates data-driven wavelets
- dwtos.m: one-stage discrete wavelet transform
- idwtos.m: inverse one-stage discrete wavelet transform
- u2v.m: creates high-pass filter from low-pass filter
- v2u.m: creates low-pass filter from high-pass filter
This distribution also contains the data needed to recreate the results in the cited paper, and three MATLAB scripts that recreate the main results and demonstrate how to calculate data-driven wavelets with the above functions:
- exampleGaussianWhiteNoise.m: recreates main results for Gaussian white noise data
- exampleKS.m: recreates main results for Kuramoto-Sivashinsky data
- exampleHIT.m: recreates main results for turbulence data
As is, exampleHIT.m will not run since the associated data is too large to host on Github. However, the cited paper explains where to obtain the required data.
If you make use of this distribution, please cite "Discovering multiscale and self-similar structure with data-driven wavelets," by D. Floryan and M. D. Graham, PNAS, 118(1), 2021.