Abstract
T. Morita, following earlier work of D. E. Newland, has shown how to construct a system of harmonic wavelets via a particular “re-orthogonalization” of the standard Fourier basis for the space L2[−π,π]. His wavelets, in real form, are based on two distinct types of scaling functions. In the present paper we consider different, but related, re-orthogonalizations leading to wavelet systems which, in real form, are based on translations of a single type of scaling function and, in addition, have very attractive properties from the viewpoint of trigonometric interpolation. The cases n even and n odd lead to distinctly different scaling functions and related trigonometric interpolation formulae.
