Precompensation for anticipated erasures in LTI interpolation systems

This paper considers compensation of anticipated erasures in a discrete-time (DT) signal such that the desired interpolation can still be accomplished, with minimum error, through a linear time-invariant (LTI) filter. The algorithms presented may potentially be useful in the compensation of a fault in a digital-to-analog converter where samples are dropped at known locations prior to reconstruction. Four algorithms are developed. The first is a general solution that, in the presence of erasures, minimizes the squared error for arbitrary LTI interpolation filters. In certain cases, e.g., oversampling and a sinc-interpolating filter, this solution is specialized so it perfectly compensates for erasures. The second solution is an approximation to the general solution that computes the optimal, finite-length compensation for arbitrary LTI interpolation filters. The third is a finite-length windowed version of the oversampled, sinc-interpolating solution using discrete prolate spheroidal sequences. The last is an iterative algorithm in the class of projection onto convex sets. Analysis and results from numerical simulations are presented.