Abstract

Operator techniques lead to spectral algorithms to compute scaling functions and wavelets associated with multiresolution analyses (MRAs). The spectral algorithms depend on the choice of pairs of suitable orthonormal bases (ONBs). This work presents the spectral algorithms for three different pairs of ONBs: Haar bases, Walsh–Paley bases and trigonometric bases. The Walsh–Paley bases connect wavelet theory and dyadic harmonic analysis. The results for trigonometric bases are the first viable attempt to do a discrete Fourier analysis of the problem.

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