Multiresolution analysis, its link to the discrete parameterwavelet transform, and its initialization

  • Authors:
  • Y.T. Chan;K.C. Ho

  • Affiliations:
  • Dept. of Electr. & Comput. Eng., R. Mil. Coll. of Canada, Kingston, Ont.;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 1996

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Abstract

By establishing an equivalence between the discrete parameter (DP) wavelet transform and the multiresolution analysis (MRA) detail coefficients, a simple derivation of the two-scale wavelet equations is given. MRA computes the DP of a signal s(t) only if the MRA inputs s(n) are samples of the inner product of s(t) and the scaling function. This is seldom true in practice. A prefiltering of s(n), as an approximate initialization, is necessary to make the MRA detail coefficients closer to the DP coefficients. A new prefiltering scheme is proposed and shown to be effective in an example