On translation invariant subspaces and critically sampled wavelet transforms (Q678239)

The use of robust representations as a solution to the translation error in the Zak domain is proposed. An iterative algorithm in the Zak domain for designing increasingly robust representations is developed. An approach for generating multiresolution subspaces that retain most of their coefficient energy as the input signal is shifted, is obtained. A typical robust subspace retains 98\% of its energy, which is a improvement over more traditional wavelet representations. Two applications are discussed: detection in multipath and discrete wavelet interpolation.