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

The reconstruction of a continuous-time signal
s(t)
from the sign of its (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 band-limited. The convergence rates obtained here are faster than those obtained previously for nonsequential estimates. The degradation in the reconstruction of the signal, due to transmission over a noisy channel, is also investigated, and bounds on the additional error are obtained.