**ABSTRACT**
###
Fast reconstruction methods for bandlimited functions from
periodic nonuniform sampling

#### Thomas Strohmer and Jared Tanner

A well-known generalization of Shannon's sampling theorem states
that a bandlimited function can be reconstructed from its periodic
nonuniformly spaced samples if the effective sampling rate is at least the
Nyquist rate. Analogous to Shannon's sampling theorem this generalization
requires that an infinite number of samples is available, which however
is never the case in practice. Most existing reconstruction methods for
periodic nonuniform sampling yield very low-order (often not even
first-order)
accuracy when only a finite number of samples is given. In this paper
we propose a fast, numerically robust, root-exponential accurate
reconstruction method. The efficiency and accuracy of the algorithm is
obtained by fully exploiting the sampling structure and utilizing
localized Fourier analysis.
We discuss applications in analog-to-digital conversion where nonuniform
periodic sampling arises in various situations. Finally we demonstrate
the performance of our algorithm by numerical examples.

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