Multiresolution approximation scale and time-shift subspaces

  • Authors:

  • Nhan Levan;Carlos S. Kubrusly

  • Affiliations:

  • Department of Electrical Engineering, University of California in Los Angeles, Los Angeles, USA 90024-1594;Catholic University of Rio De Janeiro, Rio De Janeiro, Brazil 22453-900

  • Venue:
  • Multidimensional Systems and Signal Processing
  • Year:
  • 2006

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Abstract

Multiresolution Approximation subspaces are $$\mathcal{L}^{2}(\mathbb{R})$$ -subspaces defined for each scale over all time shifts, i.e., "scale subspaces", while with respect to a given wavelet, the signal space $$\mathcal{L}^{2}(\mathbb{R})$$ not only admits orthogonal scale subspaces basis, but orthogonal "time shift subspaces" basis as well. It is therefore natural to expect both scale subspaces and time shift subspaces to play a role in Wavelet Theory and, in particular, in Multiresolution Approximation as well. This is what will be discussed in the paper.