Improved problem formulation for signal extrapolation
Steffen Paul, Josef A. Nossek · 1991
The extrapolation of a discrete-time signal is considered. Iterative algorithms for this problem require numerous iterations for accurate results. An analysis shows the very large condition number of the linear equations, and thus the slow convergence. One way to circumvent the slow convergence is to use better algorithms, such as truncated singular value decomposition (TSVD) or special conjugate gradient algorithms. An improved problem formulation is proposed. It is shown how to reduce the condition number by some orders of magnitude with a more realistic low-pass filter matrix. The modified system is solved by TSVD with uncritical dependence of the solution error on the number of singular values involved.>