论文信息 - APPROXIMATE INTERPOLATION AND THE SAMPLING THEOREM

APPROXIMATE INTERPOLATION AND THE SAMPLING THEOREM

A modified version of the sampling series is introduced for band-limited functions which converges faster than the usual sampling series. It is shown that the only polynomially bounded functions that satisfy the sampling theorem are in fact band-limited functions, so that the use of partial sums of the sampling series to interpolate polynomially bounded functions that are not band-limited will introduce interpolation errors. A proof that such errors can be made arbitrarily small for a suitably small choice of the sampling interval is presented.

Alan J. Lee

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