[Eeglablist] causal bandpassfilter with very low cutoff

[Andreas Widmann]

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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