On the dimension function of orthonormal wavelets

Orthonormal Polynomial Wavelets on the Interval

We use special functions and orthonormal wavelet bases on the real line to construct wavelet-like bases. With these wavelets we can construct polynomial bases on the interval; moreover, we can use them for the numerical resolution of degenerate elliptic operators.

Tight frame wavelets and the dimension function

On orthonormal wavelets and paraunitary filter banks

Binary tree-structured filter banks have been employed in the past to generate wavelet bases. While the relation between paraunitary filter banks and orthonormal bases is known to some extent, there are some extensions which are either not known, or not published so far. In particular it is known that a binary tree-structured filter bank with the same paraunitary polyphase matrix on all levels ...

Orthonormal Dilations of Parseval Wavelets

We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...

Orthonormal Wavelets for System Identification

A new scheme of non-parametric identification method based on orthonormal wavelets for structures with multicoupled modes is developed and presented in this paper. The advantages of using Wavelets for system identification are that good localization and hierarchical multiresolution can be achieved in both time and frequency domains. Consequently, the system model with multiple coupled modes can...