The problem of extracting a signal $x_{n}$ from a noise-corrupted
time series $y_{n} = x_{n}+e_{n}$ is considered. The signal $x_{n}$ is assumed
to be generated by a discrete-time, deterministic, chaotic dynamical system
$F$, in particular, $x_{n} = F^{n}(x_{0})$, where the initial point $x_{0}$ is
assumed to lie in a compact hyperbolic $F$-invariant set. It is shown that (1)
if the noise sequence $e_{n}$ is Gaussian then it is impossible to consistently
recover the signal $x_{n}$ , but (2) if the noise sequence consists of i.i.d.
random vectors uniformly bounded by a constant $\delta > 0$, then it is
possible to recover the signal $x_{n}$ provided $\delta < 5\Delta$, where
$\Delta$ is a separation threshold for $F$. A filtering algorithm for the
latter situation is presented.