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. The iterative procedure developed consists of using 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 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. The examples give comparable results to nonadaptive extrapolation methods without the need for a priori knowledge. For a certain spectral estimation example, the algorithm provides comparable resolution to the parametric methods with more accurate values of the relative strengths of the narrowband components