Abstract

High-frequency components that are lost when a signal s(x) of bandwidth W is low-pass filtered in sinusoid-crossing sampling are recovered by use of the minimum-negativity constraint. The lost high-frequency components are recovered from the information that is available in the Fourier spectrum, which is computed directly from locations of intersections {x i} between s(x) and the reference sinusoid r(x) = Acos(2πf r x), where the index i = 1, 2, … , 2M = 2Tf r, and T is the sampling period. Low-pass filtering occurs when f r < W/2. If |s(x)| ≤ A for all values of x within T, then a crossing exists within each period Δ = 1/2f r. The recovery procedure is investigated for the practical case of when W is not known a priori and s(x) is corrupted by additive Gaussian noise.

© 1998 Optical Society of America

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