Compactly supported sampling function for wavelet subspaces

Waiter´s sampling theorem and its extensive version by Janssen for wavelet subspaces are discussed in this paper. We give the condition that compactly supported scaling function forms compactly supported sampling function, and then point out that this condition is so strict that most compactly supported scaling functions can´t form compactly supported sampling functions, so we can´t reconstruct the compactly supported signal in practice. For non-compactly supported sampling function, we present a method to choose the parameter α to make the sampling function with fast decay, which can approximate the compactly supported sampling function. In the end, examples of the sampling function with fast decay are given