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(2pif(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 acrossing exists within each period D = 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.
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