On the extrapolation of bandlimited signals
Abstract
The determination of the Fourier Transform of a bandlimited signal in terms of a finite segment is examined. The Papoulis' Extrapolation Algorithm is extended in a broader class of signals and its convergence is considerably improved by a multiplication with an adaptive constant, chosen to minimize the mean square error in the extrapolation interval. The discrete version of the iteration is examined and then modified in order to converge to the best linear mean square estimator of the unknown signal when noise is added to the given data. The problem of determining the frequencies, amplitudes and phases of a sinusoidal signal from incomplete noisy data, is considered and the extrapolation algorithm is properly modified to estimate these quantities. The obtained iteration is nonlinear and adaptively reduces the spectral components due to noise. The adaptive extrapolation technique is applied to the problem of image restoration for objects consisting of point or line sources, and to an ultrasonic problem.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1980
 Bibcode:
 1980PhDT........69C
 Keywords:

 Extrapolation;
 Fourier Transformation;
 Frequencies;
 Signal Processing;
 Spectral Bands;
 Image Reconstruction;
 Noise Spectra;
 Signal Reflection;
 SturmLiouville Theory;
 Ultrasonics;
 Communications and Radar