A comparison of three methods for discrete-time signal extrapolation

Methods for the extrapolation of a band-limited signal based on three different approaches for solving systems of linear equations--singular value decomposition, conjugate gradients, and A-minimal iterations--are compared with respect to the computational complexity of their implementations, the effect of noise on their performance, and the manner in which each addresses the problem of a poorly conditioned system. It is observed that the solution obtained by the SVD approach is theoretically best in the least squares sense, although it is computationally the most expensive. Decreases in computational costs are paralleled by decreases in the expected and observed quality of the extrapolation produced by the three methods. The use of decimation with the SVD approach to reduce computation as discussed in previous work [1] is seen to make SVD competitive with the two conjugate direction techniques in this respect.