Add a Wavelet-Based Method #164
Description
Yet another smoothing method to take derivatives of noisy data. Seems like it might have nice properties, computing the derivative at multiple resolutions and working for aperiodic functions. The frequency content of a wavelet is fairly consistent across its domain too, so there's less potential for poor edge fits due to increased noise sensitivity in those regions, like with polynomial bases.
https://www.sciencedirect.com/science/article/abs/pii/S0169743903001370
For local, Gaussian wavelets, it seems essentially like RBFDiff, although in that case you pick a single radius, so there's no multiscale. Are they really doing the same thing? Would other wavelets be interesting to implement? Apparently even Haar wavelets work for this, which I have trouble picturing since they're piecewise constant, but they're not the best choice, which is apparently "bi-orthogonal" wavelets.