BAND-LIMITED EXTRAPOLATION USING TIME-BANDWIDTH DIMENSION

The problem of extrapolating discrete-index bandlimited signals from a finite number of samples is addressed in this paper. The algorithm pr esented in this paper exploits the fact that the set of bandlimited si gnals that are also essentially time-limited is approximated well by a low-dimensional linear subspace. This fact, which is well known for o ne-dimensional (1-D) signals with contiguous passbands and time-concen tration intervals, is established for a more general class of multidim ensional (m-D) signals with discontiguous passbands and discontiguous time-concentration regions. A criterion is presented for determining t he dimension of the approximating subspace and the minimax optimal sub space itself based on knowledge of the passband, time-concentration re gions, energy concentration factor, and bounds on the tolerable extrap olation error. The extrapolation is constrained to lie in this subspac e, and parameters characterizing the extrapolation are obtained from t he data by solving a linear system of equations. For certain sampling patterns, the system is ill conditioned, and a second-rank reduction i s needed to reduce the deleterious effects of observation noise and mo delling error. A novel criterion for rank selection based on known bou nds on noise power and modelling error is presented. The effectiveness of the new algorithm and the rank selection criterion are demonstrate d by means of computer simulations.