Orthogonalization and isospectral approximation
Ola Bratteli, Palle E. T. Jørgensen · Applied and numerical harmonic analysis · 2002
The need for the more general wavelet families is motivated already on the grounds of symmetry in the dyadic case, as follows: recall that in order to obtain compactly supported wavelets that are continuous as well as symmetric, or antisymmetric, one has to abandon orthogonality. This was noted in Chapter 2, while in the exercises of Chapter 1, we recall that the splines serve as examples with symmetry, or antisymmetry. The theorems which exclude an axis of antisymmetry for the real-valued continuous and compactly supported dyadic wavelet functions center around [Dau92, Theorem 8.1.4 and Remark 2, p. 253].