Restoring lost samples from an oversampled band-limited signal

When a band-limited signal is sampled at its Nyquist rate, each sample is independent. When sampled in excess of that rate, the samples become dependent. Thus, if one or more samples are lost, they can be recovered from the remaining known values. Using Gerchberg's iterative algorithm applied to interpolation, we derive a closed form expression by which a finite number of data points can be regained from the remaining data in a uniformly oversampled signal. A second restoration algorithm-based on an observation due to Howard-is also presented.