Positive hybrid sampling in wavelet subspaces

It is well known that the Shannon sampling theorem can be put into a wavelet context. But it has also been shown that for most wavelets, a non-negative summability function for the associated subspaces exists. Translation of these are used in a series with sampling coefficients to get a “hybrid” series each of whose terms is non-negative. Such series converge, avoid integration, and eliminate the Gibbs phenomenon