On Truncation Error Bounds for Sampling Representations of Band-Limited Signals
- 1 November 1966
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Aerospace and Electronic Systems
- Vol. AES-2 (6) , 640-647
- https://doi.org/10.1109/taes.1966.4501956
Abstract
All sampling representations of band-limited signals involve infinite sums. The truncation error associated with a given representation is defined as the difference between the signal and an approximating sum utilizing a finite number of terms. In this paper truncation error is expressed as a contour integral for Lagrange interpolation, general Hermite interpolation, the Shannon series (cardinal series), the Fogel derivative series, and multidimensional sampling expansions. Truncation error bounds are obtained under various constraints on the signal magnitude, spectral smoothness, and energy content.Keywords
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