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High-pass filtering

The data to be considered is the FMRI time series at each voxel following motion correction. The raw motion-corrected time series have a considerably coloured noise structure, the majority of which occurs at low frequency. Therefore, in this paper our approach is to perform high-pass filtering to remove the worst of the low frequency components. This is also beneficial since it is the low frequency deterministic trends in the time series which contribute most to violating an assumption of second-order stationarity.

High-pass filtering can be performed by incorporating such things as a discrete cosine transform set (DCT) into the design matrix $ \mathbf{X}$ or into the matrix $ \mathbf{S}$ (Friston et al., 2000). However, such techniques produce large end-effects and so we prefer to use a non-linear filter as proposed by Marchini and Ripley (2000). This approach fits and removes Gaussian-weighted running-lines of fixed width using a least squares fit and was found to be a reliable method of trend removal in Marchini and Ripley (2000). As in Marchini and Ripley (2000), the width of the Gaussian is chosen to be twice the cycle length when using boxcar or single event with fixed inter-stimulus interval(ISI)(Bandettini and Cox, 2000) designs. However, for randomised ISI single event designs (Burock et al. (1998), Dale and Buckner (1997) and Dale (1999)) the situation is not as clear. This is because the signal contains power at virtually all frequencies (see figure 10(b)). Hence, a compromise is used by setting the full-width half-maximum (FWHM) to 45 scans. This removes the worst of the low frequency trends, allowing sensible autocorrelation modelling, whilst removing negligible power from the signal. Such nonlinear high-pass filtering is performed as a preprocessing step on all data sets subsequently used in this paper.


next up previous
Next: Autocorrelation Estimation Up: Methods Previous: Strategies for Dealing with
Mark Woolrich 2001-07-16