Skip to main content
eScholarship
Open Access Publications from the University of California

A wavelet "time-shift-detail" decomposition

  • Author(s): Levan, N
  • Kubrusly, Carlos S
  • et al.
Abstract

\begin{abstract}We show that, with respect to an orthonormal wavelet $\psi(.)\in \L^{2}(\RR),$ any $f(.)\in\L^{2}(\RR)$ is, on the one hand, the sum of its ``layers of details'' over all time-shifts, and on the other hand, the sum of its layers of details over all scales. The latter is well known and is a consequence of a wandering subspace decomposition of $\L^{2}(\RR)$ which, in turn, resulted from a wavelet Multiresolution Analysis (MRA). The former has not been discussed before. We show that it is a consequence of a decomposition of $\L^{2}(\RR)$ in terms of reducing subspaces of the dilation-by-2 shift operator. \end{abstract}

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View