Cheung-Marks theorem

The Cheung-Marks Theorem specifies conditions where restoration by the sampling theorem can become ill-posed. It offers conditions whereby "reconstruction
error with unbounded variance when a bounded variance noise
is added to the samples."
Background
In the sampling theorem, the uncertainty of the interpolation as measured by noise variance is the same as the uncertainty of the sample data when the noise is i.i.d. In his classic 1948 paper founding information theory, Claude Shannon offered the following generalization of the sampling theorem.
Although true in the absence of noise, many of the expansions proposed by Shannon become ill-posed. A small amount of noise on the data renders restoration unstable. Such sampling expansions are not useful in practice since sampling noise, such as quantization noise, rules out stable interpolation and therefore any practical use.
Example
Shannon's suggestion of simultaneous sampling of the signal and its derivative at half the Nyquist rate results in well behaved interpolation. The Cheung-Marks theorem shows counter intuitively that interlacing signal and derivative samples makes the restoration problem ill-posed.
The Theorem
Generally, the Cheung-Marks theorem shows the sampling theorem becomes ill-posed when the area (integral) of the squared magnitude of the interpolation function over all time is not finite.

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