MULTIRESOLUTION ANALYSIS, ITS LINK TO THE DISCRETE PARAMETER WAVELET TRANSFORM, AND ITS INITIALIZATION

By establishing an equivalence between the discrete parameter (DP) wav elet transform and the multiresolution analysis (MRA) detail coefficie nts, a simple derivation of the two-scale wavelet equations is given. MRA computes the DP of a signal s(t) only if the MRA input s(n) are sa mples of the inner product of s(t) and the scaling function. This is s eldom true in practice. A prefiltering of s(n), as an approximate init ialization, 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.