Here Maximal Overlap Discrete Wavelet Transforms (MODWTs) are computed with the 'modwt' function of the R package 'wavelets'.

Multi-Resolution Analysis based on MODWT is carried out and smooths and details at each scale level can be displayed. The following figure is a reminder of how the algorithm produces smooths (S1, S2,S3, ...) and details (D1,D2, D3, ...) in what is called the pyramid algorithm.


For more information about Discrete Wavelet Transforms, please refer to:

Percival, Donald B, and Andrew T Walden. 2006. Wavelet Methods for Time Series Analysis. Vol. 4. Cambridge University Press.