Abstract
The chapter discusses the relation between finite-dimensional models of non-uniform sampling as they are used for numerical algorithms and the infinite-dimensional theory of non-uniform sampling of bandlimited functions. It is shown that interpolation and approximation by trigonometric polynomials provides a correct finite-dimensional discretization of the sampling problem for bandlimited functions. The results hold in arbitrary dimension and in particular they validate some recent fast reconstruction methods in dimension two.
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© 2001 Springer Science+Business Media New York
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Gröchenig, K. (2001). Non-Uniform Sampling in Higher Dimensions: From Trigonometric Polynomials to Bandlimited Functions. In: Benedetto, J.J., Ferreira, P.J.S.G. (eds) Modern Sampling Theory. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0143-4_7
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DOI: https://doi.org/10.1007/978-1-4612-0143-4_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6632-7
Online ISBN: 978-1-4612-0143-4
eBook Packages: Springer Book Archive