High pass filtering is used to remove the worst of the
low frequency noise in the FMRI time series. Here we are using the non-linear
high-pass filtering discussed in the previous section.
In figure 3(b) a FWHM of 40 scans was used and has the effect
of removing the lower peak and pushing
the whole histogram to higher values. This shift to higher
values represents a decrease in the positive
autocorrelation in the data; this corresponds to a decrease in the
parameter variances, as desired. The use of high-pass filtering
reduces the low frequency noise and non-stationarity
of the time series, making the estimation of the autocorrelation
more robust and valid. However, having used a non-linear high-pass
filter, the power spectral density of the time series has been
shaped in such a way that it is not easily modelled by a low order
parametric AR model.