[Eeglablist] Effect of anti-aliasing low-pass filter on connectivity analysis

Andreas Widmann widmann at uni-leipzig.de
Tue Aug 25 02:50:03 PDT 2015


Dear Makoto,

> I have been wondering about this but keep forgetting to ask you about it:
> 
> > no stopband (below Nyquist)
> 
> Why do you need to avoid having a stopband below Nyquist?
> I appreciate your kind help.
This refers to the notion by Barnett and Seth (2011; quoted below) that „low power in stop band“ is one primary cause for the large increase in required empirical model order and thus, responsible for the problems introduced by filtering in Granger causality analysis.

This only applies to GC analysis. For standard ERP-analysis it might be recommended to have a considerably lower anti-aliasing filter cutoff and a stopband below Nyquist to improve signal fidelity. In the repaired pop_resample function anti-aliasing cutoff and transition band/roll-off can be adjusted on the command line.

Hope this helps! Best,
Andreas

> Makoto
> 
> 
> On Wed, Jun 24, 2015 at 4:02 AM, Andreas Widmann <widmann at uni-leipzig.de> wrote:
> Dear Makoto,
> 
> to my understanding filter causality and Granger causality are not directly related. The output of a causal linear filter is identical to the output of a non-causal linear filter but shifted on the time axis (delayed; but equally across channels and bands!). Non-linear (here min phase) filters distort the phase spectrum and should, to my understanding, not be used for GC analysis.
> 
> Barnett and Seth (2011, J Neurosci Meth) show that GC is in theory (but not in practice) invariant under filtering. They do recommend filtering to achieve stationarity (e.g., drift, line noise; also in recent 2015 J Neurosci paper). The main problem with filtering and GC is the increase in required model order ("We have shown that a primary cause is the large increase in empirical model induced by filtering; high model orders become necessary in order to properly fit the modified aspects of the power spectrum (low power in stop band, steep roll-off, etc.).“).
> 
> That is, to my understanding for a carefully designed anti-aliasing filter (linear, zero-phase) the impact should be limited. The anti-aliasing filter as it is implemented in the repaired pop_resample function (in develop but not yet in eeglab13 branch) will have no stopband (below Nyquist) and a rather shallow roll-off (and low order) with default cutoff (fc = 0.9 * Nyq) and transition band width (df = 0.2 * Nyq). The cutoff and transition band width can be manually defined by the user, so you can try to apply a more shallow roll-off, e.g. with fc = 0.8 and df = 0.4. This conclusion should, however, be actually tested with a simulation. From a practical perspective any M/EEG signal has been filtered with an anti-aliasing filter.
> 
> > As the ERP handbook by Luck (or his other book) recommends, anti-aliasing should better have the margin of 4-5 times of the new sampling rate e.g. if you downsample signlas to 250 Hz, anti-aliasing low-pass at 125 Hz is the standard, but recommendation is 75 Hz or even 50 Hz. Well, I haven't tested it myself so I am not sure what bad it would do if I use 125 Hz (any comment on this, anyone?) but in this case, I guess the anti-aliasing low-pass filter does affect the subsequest connectivity analysis--am I correct (assuming that I analyze EEG up to 50 Hz)?
> To my understanding this conservative oversampling ratio is intended to improve signal fidelity (resolution, noise) rather than anti-aliasing alone. Given the result demonstrated by Barnett and Seth I would not recommend applying a lowpass filter with a stopband below Nyquist.
> 
> Best,
> Andreas
> 
> > Am 24.06.2015 um 02:59 schrieb Makoto Miyakoshi <mmiyakoshi at ucsd.edu>:
> >
> > Dear Iman,
> >
> > > Using causal filter may adversely effect the direction of information
> >
> > flow in the GC analysis. It is recommended that one use a
> >
> > non-causal filter (for example, finite impulse response filters) with
> >
> > zero phase lag
> >
> >
> > Really? The impulse response of the non-causal FIR filter spreads in both ways in the time domain, which means info of future events leak to past... I thought using causal filter with minimum phase makes more sense.
> >
> > Makoto
> >
> > On Tue, Jun 23, 2015 at 4:29 PM, Iman Mohammad-Rezazadeh <irezazadeh at ucdavis.edu> wrote:
> > http://journal.frontiersin.org/article/10.3389/fnhum.2015.00194/abstract
> >
> >
> >
> > Using causal filter may adversely effect the direction of information
> >
> > flow in the GC analysis. It is recommended that one use a
> >
> > non-causal filter (for example, finite impulse response filters) with
> >
> > zero phase lag (Mullen et al., 2012, Coben and Rezazadeh, 2015)
> >
> >
> >
> >
> >
> > From: eeglablist-bounces at sccn.ucsd.edu [mailto:eeglablist-bounces at sccn.ucsd.edu] On Behalf Of Makoto Miyakoshi
> > Sent: Tuesday, June 23, 2015 2:07 PM
> > To: Vito De Feo
> > Cc: EEGLAB List
> > Subject: Re: [Eeglablist] Effect of anti-aliasing low-pass filter on connectivity analysis
> >
> >
> >
> > Thank you Vito for your response. Forgive me to ask you one more question.
> >
> >
> >
> > As the ERP handbook by Luck (or his other book) recommends, anti-aliasing should better have the margin of 4-5 times of the new sampling rate e.g. if you downsample signlas to 250 Hz, anti-aliasing low-pass at 125 Hz is the standard, but recommendation is 75 Hz or even 50 Hz. Well, I haven't tested it myself so I am not sure what bad it would do if I use 125 Hz (any comment on this, anyone?) but in this case, I guess the anti-aliasing low-pass filter does affect the subsequest connectivity analysis--am I correct (assuming that I analyze EEG up to 50 Hz)?
> >
> >
> >
> > Makoto
> >
> >
> >
> > On Mon, Jun 22, 2015 at 9:31 AM, Vito De Feo <vito.defeo at zmnh.uni-hamburg.de> wrote:
> >
> > Dear Makoto,
> > this will not affect the connectivity analysis if the frequency of interest are far from the Nyquist frequency. For example if you downsample to 500 Hz (Nyquist freq = 250 Hz) you will have no problem in the band 0-100 Hz.
> > Best
> > Vito
> >
> >
> > Il giorno 20/giu/2015, alle ore 00:28, Makoto Miyakoshi ha scritto:
> >
> > > Dear List,
> > >
> > > If I use zero-phase low-pass filter for anti-aliasing, does it affect the subsequent connectivity analysis? I ask this because EEGLAB pop_resample() automatically applies it. If it does, is there a workaround? Should I use minimum phase causal filter for anti-aliasing?
> > >
> > > --
> > > Makoto Miyakoshi
> > > Swartz Center for Computational Neuroscience
> > > Institute for Neural Computation, University of California San Diego
> >
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> >
> >
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> > Makoto Miyakoshi
> > Swartz Center for Computational Neuroscience
> > Institute for Neural Computation, University of California San Diego
> >
> >
> >
> >
> > --
> > Makoto Miyakoshi
> > Swartz Center for Computational Neuroscience
> > Institute for Neural Computation, University of California San Diego
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> 
> 
> 
> 
> -- 
> Makoto Miyakoshi
> Swartz Center for Computational Neuroscience
> Institute for Neural Computation, University of California San Diego
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