Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals

Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals

The paper is concerned with Shannon sampling reconstruction formulae of derivatives of bandlimited signals as well as of derivatives of their Hilbert transform, and their application to Boas-type formulae for higher order derivatives. The essential aim is to extend these results to non-bandlimited s...

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Bibliographic Details
Main Authors: Rudolf L. Stens, Gerhard Schmeisser, Paul L. Butzer
Format: Article
Language:English
Published: MDPI AG 2012-11-01
Series:Entropy
Subjects:
sampling formulae
differentiation formulae
non-bandlimited functions
aliasing error
Hilbert transforms
formulae with remainders
derivative-free error estimates
Bernstein’s inequality
Online Access:http://www.mdpi.com/1099-4300/14/11/2192

Internet

http://www.mdpi.com/1099-4300/14/11/2192

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