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.
