Daubechies wavelets are such incredibly strange and beautiful objects, particularly for how deviant they are compared to everything you are typically familiar with when you are starting your signal processing journey… if it’s possible for a mathematical construction to be punk, then it would be the Daubechies wavelets.
Thank you for that, I was looking for exactly this. I consider myself fairly competent in a bunch of DSP topics (Fourier and Laplace, and respectively the z-transform, are no mystery to me), but I have a few problems to solve where I feel that wavelets could be very beneficial.
I was inspired by her work in the 2010s and have since used the wavelets to denoise time-series with great success [0]. I believe that learning about wavelet transforms is both beneficial in itself, but also beneficial in understand the ubiquitous Fourier transform.
I checked your post and it is not clear to me what is the added value of wavelets in the setting you used to illustrate.
The noise was i.i.d. random normal variates with the mean of -0.5 which is exactly like shifting the signal by -0.5 and then adding zero-centered noise. Well, let's say you shift by -10 or -1000 instead - there's no way to recover the magnitude of that shift unless one has additionnal information (like the true signal should be zero mean for instance).
Almost 40 years after the creation of Daubechies wavelets, I know we should wait a bit before awarding people since we can't always know in advance what would stick as important and what would just be temporary hype, but 40 years is too much IMHO…
Is it accurate to say that wavelets were a promising avenue of research in the 1990s but interest in them has kind of died because they were obsoleted by CNNs?
