EXTRAPOLATION AND SPECTRAL ESTIMATION WITH ITERATIVE WEIGHTED NORM MODIFICATION

An algorithm is developed to define, from the data samples themselves, a frequency weighted norm to use in minimum weighted norm extrapolation. Normally, the weight would be choosen to incorporate a priori knowledge of the bandwidth and shape of the spectrum of the signal to be estimated. The iterative procedure developed in this paper uses a periodogram spectrum estimate obtained from some samples of the signal estimate/extrapolation found at one iteration to define the weight that is used to estimate at the next iteration. This algorithm usually converges in less than 10 iterations to an extrapolation which is characterized as a nonparametric frequency-stationary extension of the data. The technique presented here is similar but more versatile than the Papoulis-Chamzas adaptive extrapolation procedure since it is not restricted to narrow-band signals. The frequency resolution and extrapolation length are controlled by the length of a time-domain window used to obtain smooth spectral estimates between iterations. Examples are provided to illustrate the use of the algorithm for interpolation/extrapolation. These examples gives comparable results to nonadaptive extrapolation methods without the need for a priori knowledge. For the spectral estimation example of Kay and Marple, it provides comparable resolution to the parametric methods with more accurate values of the relative strengths of the narrow-band components.