Constructive realizable multiresolution wavelet-like systems based on multi-windows spline-type spaces.

In this paper, we present a constructive realizable procedure for obtaining a multiresolution wavelet-like system in the framework of stability for spline-type spaces, considering only the generators that prominently intersect the spectrum of the signal to be approximated and stable under deformations through frequency shifts. The realizable system constructed in this way, can analyse jointly three different features of a signal namely time, scale and frequency. We present numerical tests and a detailed complexity analysis to compare the performances of our method against standard constructions.