Error of linear estimation of lost samples in an oversampled band-limited signal

A finite number of lost samples from an oversampled band-limited signal can be restored from the remaining samples. This paper explores the noise sensitivity of a linear algorithm that performs such restoration. Even though the problem is well posed, restoration noise level can become prohibitively high for a) sampling rates close to the Nyquist rate, and b) too many lost samples. Numerical results of restoration noise level are given for the cases of one lost sample, two (not necessarily adjacent) samples and a sequence of M adjacent lost samples. The effects of both truncation and noise are evaluated for the case of a single lost sample in a stochastic signal. The results are compared with the corresponding minimum mean-square error of the lost sample. Although suboptimal, the truncated lost sample sampling estimate is more straightforward computationally and does not require detailed knowledge of the signal or noise second-order statistics.