Minimum Norm Least Squares Extrapolation Estimate for Discrete (a,b,c,d)-Bandlimited Signals

This letter investigates the extrapolation problem of discrete (
a
,
b
,
c
,
d
)-bandlimited signals. Based on operator notations, we first show that the extrapolation problem amounts to finding an admissible solution of an under-determined system. Then the minimum norm least squares (MNLS) solution is shown to be an admissible extrapolation estimate. Besides, singular value decomposition method is used to set up an extrapolation formula which guarantees that the extrapolation result achieves the MNLS estimate. An iterative extrapolation algorithm is also proposed to achieve the MNLS estimate. Finally, numerical results are given to demonstrate the efficiency of the proposed extrapolation algorithms.