Signal recovery in sinusoid-crossing sampling by use of the minimum-negativity constraint

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) = A cos(2 pi f(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)\ less than or equal to A for all values of x within T, then a crossing exists within each period Delta = 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. (C) 1998 Optical Society of America.