The reconstruction of analog signals from the sign of their noisy samples

The reconstruction of continuous-time signals s(t) from the sign of their (deliberately) contaminated samples is considered. Sequential, generally nonlinear estimates of s(t) are established and their performance is studied; error bounds and convergence rates are derived. The signal s(t) need not be bandlimited. The convergence rates obtained here are faster than those obtained for nonsequential estimates. The degradation in the reconstruction of the signal, due to transmission over an arbitrary noisy channel, is also investigated and bounds on the additional error are obtained.