Aliasing Error For Shannon Series Based On Local Sampling Approximation With Common Smooth Function

A bandlimited signal function can be totally reconstructed by Shannon cardinal series. This is a hot research area in communication engineering and mathematics. Because the reconstruction by Shannon cardinal series need infinite samples, which can not achieve in the actual situation. We tend to use its subtotal to approximate the signal function, which caused the truncation error is one of our research problem. But in the real situation, there are lots of non-bandlimited functions wanna to be refactored by Shannon cardinal series. Undoubtedly, we would focus on the aliasing error. Now, using Shannon caidinal series to approximate the function that belongs to the space of B_?,p?R?,W_p^r?R? and B_v,p?R^d?, the truncation error and aliasing error has lucubrated. Here, following the above work, we use Shannon cardinal series to approximate a commonly smooth function f, based on local sampling, study the truncation error and aliasing error and estimate their community, that ishere,...