[FieldTrip] removing EEG 1/f spectral power

[Robert Oostenveld]

Dear David,

Often we look at the contrast between two experimental conditions, in which then the 1/f disappears in the contrast, so we don't have to bother. But there are indeed valid cases where you want it out, such as detecting peaks that sit on a 1/f flank. A simple trick that you can use is based on the following idea:

say  f(t) = sin(w*t), 
then df/dt = w*cos(w*t)

So taking the derivative of a sine multiplies the output with "w" , which is the frequency in radians per second. This applies to each frequency. Taking the derivative is a linear operation, so if your data consists of the sum of many sine-waves (which is the premise for Fourier analysis), taking the derivative of the data is equivalent to taking the derivative of all seperate sine-wave contributions to your data. The consequence hence is that the derivative in time results in the Fourier spectrum at frequency f being multiplied by f (for any frequency). So the 1/f effect in the spectrum is counteracted by a 1*f effect of the time-domain derivative.

In ft_preprocessing you can use cfg.derivative=yes to get the desired result. 

best regards
Robert

PS this can be considered as estimating and removing a 1-st order AR model from the data, except that we already know what the AR model parameters are. It can also be considered as a high-pass FIR filter with a filter kernel that is [-1 1].


On 20 Oct 2011, at 4:01, David Groppe wrote:

> 
> Hi  FieldTrippers,
>  I am interested in studying the spectral peaks in resting EEG.
> Identifying these peaks is complicated by the 1/f distribution of EEG
> power.  Do any of you have suggestions for removing the 1/f
> distribution to better reveal peaks?  I've seen people suggest
> autoregressive modelling or applying high pass filters but in the
> couple of attempts I've seen the results look fair.
>   much appreciated,
>     -David
> 
> 
> 
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