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

[Andreas Widmann]

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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> --
> 
> 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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