A one-step band-limited extrapolation procedure is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed scheme is to expand the known signal segment based on a band-limited basis function set and then to generate a set of Empirical Orthogonal Functions (EOF’s) adaptively from the sample values of the band-limited function set. Simulation results indicate that, in addi- tion to the attractive adaptive feature, this scheme also appears to guarantee a smooth result for inexact data, thus suggesting the robustness of the proposed procedure. A one-step band-limited extrapolation procedure is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed criterion is to expand the known signal segment based on a band-limited basis function set and then to generate a set of Empirical Simulation results indicate that, in addi- tion to the attractive adaptive feature, this scheme also appears to guarantee a smooth result for inexact data, suggesting suggesting the robustness of the proposed procedure.