Ten lectures on wavelets
Adapted wavelet analysis from theory to software
Adapted wavelet analysis from theory to software
Wavelets: tools for science & Technology
Wavelets: tools for science & Technology
Heisenberg groups: a unifying structure of signal theory, holography and quantum information theory
The Korean Journal of Computational & Applied Mathematics
Analysis and Probability: Wavelets, Signals, Fractals (Graduate Texts in Mathematics)
Analysis and Probability: Wavelets, Signals, Fractals (Graduate Texts in Mathematics)
Entropy-based algorithms for best basis selection
IEEE Transactions on Information Theory - Part 2
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Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L^2(0,1) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the Hilbert space of square-integrable functions on the unit-interval, both with respect to Lebesgue measure, and also with respect to a wider class of self-similar measures @m. That is, we consider recursive and orthogonal decompositions for the Hilbert space L^2(@m) where @m is some self-similar measure on [0,1]. Up to two specific reflection symmetries, our scheme produces infinite families of orthonormal bases in L^2(0,1). Our approach is as versatile as the more traditional spline constructions. But while singly generated spline bases typically do not produce orthonormal bases, each of our present algorithms does.