Periodic Nonuniform Sampling in Shift-Invariant Spaces

Hogan, Jeffrey A. and Lakey, Joseph D. (2006) Periodic Nonuniform Sampling in Shift-Invariant Spaces. In: Harmonic Analysis and Applications. Applied and Numerical Harmonic Analysis (V). Birkhäuser Boston, pp. 253-287. ISBN 978-0-8176-4504-5

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    This paper reviews several ideas that grew out of observations of Djokovic and Vaidyanathan to the effect that a generalized sampling method for bandlimited functions, due to Papoulis, could be carried over in many cases to the spline spaces and other shift-invariant spaces. Papoulis' method is based on sampling output of linear, time-invariant systems. Unser and Zerubia formalized Papoulis' approach in the context of shift-invariant spaces. However, it is not easy to provide useful conditions under which the Unser-Zerubia criterion provides convergent and stable sampling expansions. Here we review several methods for validating the Unser-Zerubia approach for periodic nonuniform sampling, which is a very special case of generalized sampling. The Zak transform plays an important role.

    Item Type: Book Section
    Additional Information: The book is dedicated "in honor of John J. Benedetto"
    Subjects: 42-xx Fourier analysis
    Faculty: UNSPECIFIED
    Depositing User: Mr Christopher Maitland
    Date Deposited: 27 Jun 2011 15:33
    Last Modified: 27 Jun 2011 15:33

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