Unitary mappings between multiresolution analysis of L 2 (R) and a parameterization of low-pass filters
Manos Papadakis · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
This paper examines classes of unitary operators of L2(R) contained in the commutant of the shift operator, such that for any pari of multiresolution analyses of L2(R) there exists a unitary operator in one of these classes, which maps all the scaling functions of the first multiresolution analysis to scaling functions of the other. We use these unitary operators to provide an interesting class of scaling functions. We show that the Dai-Larson unitary parameterization of orthonormal wavelets is not suitable for the study of scaling functions. These operators give an interesting relation between low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary operators acting on L2([ -(pi) , (pi) ]), which we characterize. Using this characterization we recapture Daubechies' orthonormal wavelets by passing the spectral factorization process.