  The information flow-based quantitative causality analysis has been widely
applied in different disciplines because of its origin from first principles,
its concise form, and its computational efficiency. So far the algorithm for
its estimation is based on differential dynamical systems, which, however, may
make an issue for coarsely sampled time series. Here, we show that for linear
systems, this is fine at least qualitatively; but for highly nonlinear systems,
the bias increases significantly as the sampling frequency is reduced. This
paper provides a partial solution to this problem, showing how causality
analysis is assured faithful with coarsely sampled series when, of course, the
statistics is sufficient. An explicit and concise formula has been obtained,
with only sample covariances involved. It has been successfully applied to a
system comprising of a pair of coupled R\"ossler oscillators. Particularly
remarkable is the success when the two oscillators are nearly synchronized.
