  Consider a time series of signal measurements $x(t)$, having components $x_k
\mbox{ for } k = 1,2, \ldots ,N$. This paper shows how to determine if these
signals are equal to linear or nonlinear mixtures of the state variables of two
or more statistically-independent subsystems. First, the local distribution of
measurement velocities ($\dot{x}$) is processed in order to derive $N$ local
vectors at each $x$. If the data are separable, each of these vectors is
directed along a subspace traversed by varying the state variable of one
subsystem, while all other subsystems are kept constant. Because of this
property, these vectors can be used to determine if the data are separable,
and, if they are, $x(t)$ can be transformed into a separable coordinate system
in order to recover the time series of the independent subsystems. The method
is illustrated by using it to blindly recover the separate utterances of two
speakers from nonlinear combinations of their waveforms.
