Sampling sums based on coiflets

摘要

This paper is concerned with sampling sums through a class of wavelets (the coiflets) constructed by I. Daubechies. Comparing with the Shannon's sampling sum with the function, the advantage of the kernels based on wavelets is that they have compact support, the approximation, behaviour of the sampling sums depends only on local informatjon of the function being sampled. Moreover, because the kernel satisfies a two scale equation, there is a fast algorithm for the evaluation of the sampling sum.