Signal Recovery and the Large Sieve

Abstract

Inequalities are developed for the fraction of a bandlimited function’s $L_p $ norm that can be concentrated on any set of small “Nyquist density.” Two applications are mentioned. First, that a bandlimited function corrupted by impulsive noise can be reconstructed perfectly, provided the noise is concentrated on a set of Nyquist density $ < 1/\pi $; second, that a wideband signal supported on a set of Nyquist density $ < 1/ \pi$ can be reconstructed stably from noisy data, even when the low-frequency information is completely missing.