Energy concentration in band-limited extrapolation

Abstract

The authors present a novel bandlimited extrapolation method that incorporates qualitative prior knowledge of the distribution of signal energy in both the time domain (spatial domain) and the frequency domain. The extrapolation is easily computed by simple noniterative algorithm. The prior information is incorporated by means of a weighted energy measure, and the resulting solution is derived by straightforward Hilbert space optimization. The algorithm accommodates complex-valued sequences, nonuniform sampling, and arbitrary spectral support and is applicable in one or several dimensions. Many existing extrapolation algorithms are noted as special cases. Examples of signal extrapolation and spectrum estimation using the new algorithm are given in one and two dimensions, algorithm modification for noisy data is investigated, and error bounds are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>