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.
Highlights
Since Shannon introduced the sampling series in the context of communication in the land-mark study (Shannon, 1948), the Shannon sampling series has become more and more important
Motived by Butzer and Lei (1998), we consider the sampled values which are the results of a linear functional and its integer translates acting on a undergoing signal (Burchard and Lei, 1995)
This model covers jitter errors, amplitude errors and the errors arising from sampled values obtained by averaging a signal (Boche, 2010)
Summary
Since Shannon introduced the sampling series in the context of communication in the land-mark study (Shannon, 1948), the Shannon sampling series has become more and more important. The theorem states that a band-limited signal can be exactly recovered from its sample values. In this study we investigate the approximation sampling series with measured sampled values for not band-limited functions from Besov class and obtain the uniform bound of the truncation errors.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Research Journal of Applied Sciences, Engineering and Technology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
