[Eeglablist] causal bandpassfilter with very low cutoff

[Andreas Widmann]

Hi Sophie,

most likely the problem is filtering in single precision. IIR filters are prone to accumulate numerical error and indeed the suggested 4th order filter will be instable with single precision. Try converting the EEG.data to double precision first.

The following test script should work:

%%
% Create two random data channels, one with DC offset, one with drift
EEG.data(1, :) = single(randn(1, 10000) + 100);
EEG.data(2, :) = single(randn(1, 10000) +  linspace(1, 100, 10000));
plot(EEG.data') 
hold all

% Generate the filter
[b, a] = butter(4, 0.1 / (128 / 2), 'high');

% Filter (along 2nd dimension!)
EEG.data = filter(b, a, double(EEG.data), [], 2);

plot(EEG.data') 
%%

Please report back if this snippet does not work on your machine. If you want to omit the double function from the filter command (i.e. filter in single precision) you have to reduce filter order to 2 to get a stable filter (or use a higher cutoff).

In the filtered data of channel 1 one can see immediately see why one should not filter across DC offsets/boundaries. If you observe strong DC offsets in your data  (e.g. Biosemi raw data) you might consider subtracting the mean, detrending, or padding the raw data with a DC constant first.

Hope this helps,
Andreas

Am 08.08.2012 um 15:58 schrieb Sophie Herbst <ksherbst at googlemail.com>:

> Hi again,
> thank you for your very helpful comments. Andreas, I was trying to implement your suggestion but can't quite get it to work.
> After low-pass filtering (30Hz), downsampling (128Hz), the butterworth filter you suggested transforms large parts of the data into NaNs. 
> I think it might already go wrong with the low-pass filter. Do you have a suggestion what to use here? It should also be causal, so I tried both iirfilt and butter but apparently I was not able to put together the right combination of parameters.
> 
> Sorry for being so ignorant but my understanding of filtering is at a very early stage. 
> Sophie
> 
> 
> 
> 
> On Wed, Aug 8, 2012 at 12:13 PM, Andreas Widmann <widmann at uni-leipzig.de> wrote:
> Hi,
> 
> Sophie asked for a *causal* filter. IIR is an appropriate filter type for this purpose. Using a linear phase FIR filter, as suggested, one will introduce a long filter delay. Using a minimum-phase FIR filter one will loose linear phase anyway. Thus, it is reasonable to use IIR as the filter delay is usually considerably smaller than for minimum-phase FIR in this type of application. (I have a slight preference for Butterworth due to its good (flat) frequency response in the passband.)
> 
> See also recent contribution on causal filtering by Rousselet:
> http://www.frontiersin.org/Perception_Science/10.3389/fpsyg.2012.00131/full
> and my short comment (mainly focused on why one should not use the EEGLAB Basic FIR filter)
> http://www.frontiersin.org/Perception_Science/10.3389/fpsyg.2012.00233/full
> 
> Best,
> Andreas
> 
> Am 08.08.2012 um 10:17 schrieb Davide Baldo <davidebaldo84 at gmail.com>:
> 
> > Hi!
> >
> > I don't understand why to use a IIR filter. They always cause some (phase) distorsion.
> > I suggest you to use a FIR filter. If you use Matlab, just type "fdatool" (Filter design & analysis tool). Than select: High pass and FIR (Equiripple). Set the Srate to 512 and the Fstop to 0.01. You did not specfied which frequencies you do not want to distort. I guess you could set Fpass to 0.5 Hz (all frequencies higher than 0.5 Hz won't be modified). Then set Dstop to 0.0005 and Dpass to 0.01.
> > Now you can click on Design Filter. When done...click on File -> Export (It export the filter on Matlab workspace). Set Numerator to "HP_Filter" (it s just a name for the filter).
> >
> > Now you are ready to filter your data:
> >
> >     HP_Delay = round( mean(grpdelay(HP_filter)) ); % a FIR filter introduces a delay in the signal. you need to compensate it.
> >
> >     HP_Data = filter( HP_filter, 1, your_data ) ;  % Filter the data
> >     HP_Data  = circshift(  HP_Data , [1 -HP_Delay] ); %compensate the delay introduced by the HP filter
> >
> > I hope it helps you.
> >
> > Ciao!
> >
> > Davide.
> >
> > On Mon, Aug 6, 2012 at 6:38 PM, Andreas Widmann <widmann at uni-leipzig.de> wrote:
> > Hi Sophie,
> >
> > a 0.01 Hz highpass filter with 512 Hz sampling frequency is very extreme. My personal rule of thumb is that the srate / cutoff ratio for IIR highpass filtering should not be much higher than ~1000 (acknowledgement to BM). The problem is increased by the EEGLAB default estimation of required filter order by a very narrow transition band (defined as cutoff/3 in your case; the help text in pop_iirfilt is wrong!). The extreme filter cutoff with narrow transition band requires a high filter order (here 6), but the resulting 6th order filter is instable.
> >
> > I would suggest first downsampling the data to an as low as possible sampling frequency (after lowpass filtering the data to 1/4-1/5 of new sampling frequency!).
> >
> > Then, I would suggest filtering the data with a butterworth filter at 0.1 Hz cutoff frequency. Roll-off is a function of filter order (approx. order times -6dB/octave).
> > E.g.:
> > >> [b, a] = butter(4, 0.1 / (srate / 2), 'high')
> > for a forth order filter.
> >
> > Check frequency response with
> > >> freqz(b, a, 2^14, srate)
> > At 256 Hertz this gives a reasonable frequency response and very good DC attenuation. Downsampling your data to 128 Hz you can use the same filter for a 0.05 Hz highpass.
> >
> > Check filter stability with
> > >> zplane(b, a)
> > All poles should be inside the unit circle. If you test the 6th order butterworth filter you will see that also this filter is instable.
> >
> > Causal filtering can be done easily on the command line using the MATLAB built in filter function. Take care not to filter across boundaries/DC offsets! Filter each segment separately.
> >
> > Hope this helps, best,
> > Andreas
> >
> > Am 06.08.2012 um 17:44 schrieb Sophie Herbst <ksherbst at googlemail.com>:
> >
> > > Hi EEGlablist,
> > >
> > > I am trying to apply a causal bandpass filter with a very low cutoff (0.01Hz) to my EEG data (continuos data with ~2,700,000 points, srate = 512Hz)
> > > by using iirfilt.m:
> > >
> > > iirfilt(EEG.data, EEG.srate, 0.01, 40, 0, 0, 0, [], [], 'on')
> > >
> > > I seem to run into similar problems as described in EEGLAB Bug #1011: the default values for transition bandwidth and passband/ stopband ripple do not seem to work as
> > > the filter runs but leaves a matrix of NaNs.
> > >
> > > I have been playing around with values for the transition bandwidth etc, but I could not get a satisfying frequency response.
> > > Any idea why this is and which filter would be better to use?
> > >
> > > Thanks a lot,
> > > Sophie
> >
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