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 xi(t) to obtain new signals, say xi*(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: