Estimation of sinusoids by adaptive minimum norm extrapolation

Abstract

A series of algorithms are described in order of increasing complexity and improved performance. The original scheme of Papoulis and Chamzas (1979) serves as a model for the remaining algorithms. After a review and evaluation of their method, more direct approaches which require less iterations and perform better are then developed by considering adaptive algorithms which produce exact extrapolations at each step. Adaptive conventional bandlimited extrapolation is shown to provide good results in a much smaller number of iterations. Adaptive weighted norm extrapolation which incorporates a spectrum estimation step, rather than thresholding, is then shown to provide almost exact results in the absence of noise. A brief comparison with the principal component linear prediction method is included. The ability to incorporate a priori knowledge about the frequency locations is provided and the potential benefits of its use are briefly illustrated.<>