Interpolation, spectrum analysis, error-control coding, and fault-tolerant computing

This paper uncovers relations between the topics mentioned in the title, relations that we believe to have gone nearly unnoticed so far. More precisely, we show that four often studied problems in signal processing, spectrum analysis, information theory, and computing are closely related or even equivalent in a certain sense (if one of them can be solved, so can any of the others, and using essentially the same algorithms). The problems are (i) a nonlinear band-limited finite-dimensional interpolation problem (ii) the problem of estimating a signal that is the superposition of a finite number of harmonics (iii) an error-control coding problem in the real field, and (iv) certain techniques that occur in algorithm-based fault tolerant computing. The advantages of recognizing these problems as equivalent are obvious: the techniques commonly used in one field can be imported to the others, the duplication of research efforts is prevented, and the overall degree of understanding of the four problems increases. New algorithms are suggested as a result of these investigations.