The success of ICA for a given data set may depende crucially on
performing some application-dependent preprocessing steps. For
example, if the data consists of time-signals, some band-pass
filtering may be very useful. Note that if we filter linearly the
observed signals *x*_{i}(*t*) to obtain new signals, say *x*_{i}^{*}(*t*),
the ICA model still holds for
,
with the same mixing
matrix.

This can be seen as follows. Denote by the matrix that
contains the observations
as its columns, and similarly for
. Then the ICA model can be expressed as:

(34) |

Now, time filtering of corresponds to multiplying

(35) |

which shows that the ICA model remains still valid.