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- W2007012640 abstract "In her plenary lecture [Daubechies, I., 2005, Redundancy and robust A/D and D/A conversion (see ref. 28 Daubechies, I. Redundancy and robust A/D and D/A conversion. Proceedings of International Workshop. 2005, Samsun, Turkey. SampTA 05, Sampling Theory and Applications, pp.18Samsun: Ondokuz Mayis University, Department of Mathematics. [Google Scholar]). SampTA 05, Sampling Theory and Applications. Proceedings of International Workshop, Samsun, Turkey, 2005 (Samsun: Ondokuz Mayis University, Department of Mathematics), p. 18.] at the workshop SampTa 05, Samsun, Turkey, July 2005, Daubechies, Princeton, presented three major reasons as to why the classical sampling theorem was fully impractical for real-life signal processing. One needs infinitely many samples extended over the whole real axis, the sinc-kernel decaying much too slowly, and band limitation is a too restrictive assumption. This paper presents an approach to overcome these difficulties, which actually began to develop at Aachen 1977. The sinc-function is replaced by certain simple linear combinations of B-splines, only a finite number of samples need be available. This approach can be used to process arbitrarily continuous and even discontinuous signals. Best possible error estimates in terms of the L p -average modulus of smoothness are presented. Three typical examples exhibiting the various problems involved are worked out in detail." @default.
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- W2007012640 date "2008-01-01" @default.
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- W2007012640 title "Reconstruction of signals in<i>L</i><sup><i>p</i></sup>(ℝ)-space by generalized sampling series based on linear combinations of<i>B</i>-splines†" @default.
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- W2007012640 doi "https://doi.org/10.1080/10652460701511285" @default.
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