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IMA Journal of Mathematical Control and Information 1990 7(1):47-57; doi:10.1093/imamci/7.1.47
© 1990 by Institute of Mathematics and its Applications
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A Twisted Sampling Theorem

NIELS JUUL MUNCH

Institute of Mathematical and Physical Sciences, University of Tromso Post Box 953, 9001 Tromso, Norway

A generalized sampling theorem is proved for a set of functions f that are well behaved in the frequency domain. Specifically, let W be a positive bounded integrable function, let {chi} be a reconstruction function, and let A denote the operation of multiplication in the frequency domain by a bounded function A(s). Then coefficients hn (–{infty}<n<{infty}) are determined to minimize the maximal L2-error in an approximation scheme


for functions f ranging over the set is the Fourier of f. Formulae are given for the minimal obtainable maximal error, and the optimal choice (choices) of hn (–{infty}<n<{infty}) is characterized through its discrete Fourier transform .


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