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A signal cannot in general be reconstructed from its sign, i.e., from its hard-limited version. However, by the deliberate addition of noise to samples of the signal prior to hard limiting, it is shown that the signal can be estimated consistently from its hard-limited noisy samples as the sampling rate tends to infinity. In fact, such estimates are shown to converge with probability one to the signal and to be asymptotically normal. Although the estimates are in general nonlinear, they can be made linear by a proper choice of the noise distribution. These rather unexpected results hold for all bounded and uniformly continuous signals. In addition to the hard-limiter, such results are also established for certain monotonic and nonmonotonic nonlinearities.
Date of Publication: Jan 1981