Turing Meets Shannon: Computable Sampling Type Reconstruction With Error Control

The conversion of analog signals into digital signals and vice versa, performed by sampling and interpolation, respectively, is an essential operation in signal processing. When digital computers are used to compute the analog signals, it is important to effectively control the approximation error....

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Bibliographic Details
Published in:IEEE transactions on signal processing 2020, Vol.68, p.6350-6365
Main Authors: Boche, Holger, Monich, Ullrich J.
Format: Article
Language:English
Subjects:
Algorithms
Analog computers
Analog to digital conversion
Approximation
Approximation algorithms
Approximation error
continuous-time signal
Digital computers
discrete-time signal
effective approximation
Error analysis
Interpolation
Linear systems
Mathematical analysis
Sampling
Signal processing
Signal processing algorithms
Time signals
Time-domain analysis
Turing machines
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Summary:The conversion of analog signals into digital signals and vice versa, performed by sampling and interpolation, respectively, is an essential operation in signal processing. When digital computers are used to compute the analog signals, it is important to effectively control the approximation error. In this paper we analyze the computability, i.e., the effective approximation of band limited signals in the Bernstein spaces B π p , 1 ≤ p
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2020.3035913