nLab sampling theory

Contents

Idea

Sampling theory is a branch of harmonic analysis, especially relevant for computational harmonic analysis.

The basic result is the Kotelnikov-Whittaker-Nyquist-Shannon theorem.

wikipedia: sampling (signal processing), Nyquist-Shannon sampling theorem, Whittaker-Shannon interpolation formula, signal processing
Claude Shannon, Communication in the presence of noise, Proc. Institute of Radio Engineers 37:1, pp. 10–21, Jan. 1949 IEEE reprint
V. A. Kotelnikov, On the carrying capacity of the ether and wire in telecommunications, Material for the First All-Union Conference on Questions of Communication, Izd. Red. Upr. Svyazi RKKA, Moscow, 1933 english pdf
Kabe Moen, Hrvoje Šikić, Guido Weiss, Edward Wilson, A panorama of sampling theory, in: Excursions in Harmonic Analysis, vol. 1, Applied and Numerical Harmonic Analysis 2013, pp 107-123 doi
Hrvoje Šikić, Edward N. Wilson, Lattice invariant subspaces and sampling, Appl. Comput. Harmon. Anal. 31 (2011), no. 1, 26–43 MR2012i:42042 doi
Hernández, Eugenio; Šikić, Hrvoje; Weiss, Guido L.; Wilson, Edward N., The Zak transform(s), in: Wavelets and multiscale analysis, 151–157, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, New York, 2011 MR2012e:44005 doi
Laurent Freidel, Shahn Majid, Noncommutative harmonic analysis, sampling theory and the Duflo map in $2+1$ quantum gravity, Classical Quantum Gravity 25 (2008), no. 4, 045006 MR2009f:83058, doi

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