Min- max linear estimation of band-limited sequences from noisy observations---A deterministic approach

The representation of discrete-time waveforms as finite-energy sequences is a useful mathematical abstraction. A special class of finite-energy sequences, of particular interest to communication theorists, is the class of band-limited sequences. A linear estimation of technique for these sequences is presented. The observations are assumed to be corrupted by the components of a finite-energy, band-limited noise sequence not necessarily band-limited to the same frequencies as the signal sequence. The error metric for the estimation errors is assumed to be the energy in a linear functional of the error components, and the error-criterion, by which the merit of an estimation scheme is judged, is the maximal error over a class of band-limited and energy-constrained signal and noise sequences. An interesting finding is that the min-max estimation schemes described here have a structure similar to that of the familiar minimum mean-square error (MMSE) schemes which are designed to minimize some average error.