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Shapiro and Silverman (1960) have shown that in certain additive random sampling schemes (such as Poisson sampling), the entire covariance function is uniquely determined by the correlation sequence, thus eliminating aliasing. This enables one to estimate the entire spectral density of a continuous process by discrete sampling, and suggests the possibility of constructing sampling patterns which will also eliminate aliasing.
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Richard H. Jones (1962) studied this question.
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