Abstract

Errors appear when the Shannon sampling series is applied to reconstruct a signal in practice. In this paper, we study a general model that uses linear functional to cover several errors in one formula, and consider sampling series with measured sampled values for not band-limited signals but satisfying some decay condition. We obtain the uniform truncated error bound of Shannon series approximation for multivariate Besov class. The results show this kind of Shannon series can approximate a smooth signal well.

Keywords:

Besov class, local averages, measured sampled values, modulus of continuity, Shannon sampling theorem, truncation error,

References

Competing interests

The authors have no competing interests.

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Copyright

The authors have no competing interests.