Discretizing And Periodizing The Half-Plane
M. Holschneider · 1995
Abstract Because of the reproducing kernel identity the wavelet coefficients have an internal correlation and are therefore not independent. So it is not surprising that knowledge of the wavelet transform on a subset of the half-plane is sufficient to reconstruct the analysed function. In the following sections we consider various partial reconstruction formulas associated with different subsets of the half-plane. In particular, we consider reconstruction over strips, over zooms and cones, and over various grids. In addition, we will construct a wavelet analysis over the circle. For the sake of simplicity we will formulate everywhere in one dimension. The reader should have no difficulty in generalizing the results to wavelet transforms of functions over ℝn.