Orthonormal MRA wavelets: spectral formulas and algorithms (Q2893486)

The authors present and develop an approach to orthonormal wavelets obtained from a multiresolution analysis based on the idea that functions in \(L^2(\mathbb R)\) can be given in terms of an orthonormal basis of \(L^2[0,1)\) and integer translations thereof as well as of an orthonormal basis of \(L^2[\pm 1,\pm 2)\) and dyadic dilations of these bases. Thus the relations between the scaling function and the wavelet and algorithms for computing these are expressed in terms of the coefficients in the representation between these two expansions. The case where the bases in \(L^2[0,1)\) and \(L^2[\pm 1,\pm 2)\) are taken to be the Haar bases are studied in more detail.