[Eeglablist] eeglab causal filtering: impacts and applications?

[Cedric Cannard]

Hi all,

I am analyzing 64-channel EEG data of the pre-stimulus period [-1500 0] ms (3 conditions from 3 types of images being presented) and results will be obtained using LIMO on the ERP and ERSP data. I have been reading Andreas Widmann's papers on filtering (e.g. https://urldefense.com/v3/__https://www.frontiersin.org/articles/10.3389/fpsyg.2012.00233/full__;!!Mih3wA!VNo4GYqFILb305TK2eZbXRZWcQcgOnHzFo8Zfb510jeSOjaJCydWh45s-vE0funMJm7jiA$ ; https://urldefense.com/v3/__https://home.uni-leipzig.de/biocog/eprints/widmann_a2015jneuroscimeth250_34.pdf__;!!Mih3wA!VNo4GYqFILb305TK2eZbXRZWcQcgOnHzFo8Zfb510jeSOjaJCydWh45s-vE0fukqNL9gVw$ ), but I am still unsure I fully understand whether I should use the legacy causal FIR filter and apply a delay correction or the new minimum-phase causal filter instead. I also found this eeglablist discussion (https://sccn.ucsd.edu/pipermail/eeglablist/2013/006638.html) but it is from 2013 and there is now a beta minimum-phase causal filter available in EEGLAB, so I wonder what the new recommendations would be.

I am pretty clear about using a non-linear/causal filter and not linear/non-causal filter to avoid "introducing non-causally smeared artificial or artificially enhanced components after high-pass filtering (Fig 7D; see Acunzo et al., 2012 for discussion), or smearing post-stimulus oscillations into the pre-stimulus interval leading to spurious interpretations of pre-stimulus phase (Zoefel and Heil, 2013)."
However, regarding the causal filtering, I read: "zero-phase (non-causal) filters preserve peak latencies, while causal filters necessarily shift the signal in time. If a causal filter is needed, a non-linear minimum-phase filter should be considered as it introduces only the minimum possible delay at each frequency for a given magnitude response but distorting broadband or complex signals due to non-linearity (see Fig. 2). Causal high-pass minimum-phase (and other non-linear) filters introduce rather small delays (Fig. 2F and G) while causal low-pass (and band-pass and band-stop) filters introduce larger delays even with minimum-phase property (Fig. 2A and B), which is why they are not recommended in electrophysiology (Rousselet, 2012)."

--> This suggests I should use the minimum-phase for high-pass filtering (1 Hz) but not for low-pass filtering (50 Hz).
But further in the paper the authors say: "However, as FIR filter coefficients necessarily must be symmetric (or antisymmetric) for the filter to have linear-phase characteristic ([Rabiner and Gold, 1975](https://urldefense.com/v3/__https://www.frontiersin.org/articles/10.3389/fpsyg.2012.00233/full*B6__;Iw!!Mih3wA!VNo4GYqFILb305TK2eZbXRZWcQcgOnHzFo8Zfb510jeSOjaJCydWh45s-vE0fukJiu_LIA$ ); [Ifeachor and Jervis, 2002](https://urldefense.com/v3/__https://www.frontiersin.org/articles/10.3389/fpsyg.2012.00233/full*B2__;Iw!!Mih3wA!VNo4GYqFILb305TK2eZbXRZWcQcgOnHzFo8Zfb510jeSOjaJCydWh45s-vE0ful963Bv-w$ )), this reduction of filter delay comes at the cost of a non-linear phase response and the introduction of a systematic delay in the signal (which can not easily be compensated due to non-linear phase). The recommendation for minimum-phase causal FIR filtering, thus, should be strictly limited to the detection of onset latencies and applications where causality is required for theoretical considerations."

--> This suggests the minimum-phase filter not only introduces delays that are harder to compensate for compared to the causal FIR filter, but also that it distort complex and broadband signals? Does this mean the minimum-phase filtering might not necessarily be better than the legacy causal FIR filter for ERP/ERSP analyses?? My tests comparing the two during high-pass 1 Hz show extreme differences in the ERP plots for the same subject, obviously.
1) Which one should I use for ERP and ERSP analyses of the pre-stimulus period?
2) Can I use the standard linear zero-phase filter for low-pass filtering after a causal filter as the paper showed that low-pass filtering using causal filters introduces large delays?
My tests did not show any difference on the ERP plots compared to using only the causal filter without low-pass filtering but I haven't run more thorough tests.
3) the minimum-phase filter is called "beta" in eeglab GUI, can I confidently use it for my analysis and publication?
4) If I need to apply a delay correction (for either causal filter), how can I do it?

Thanks in advance to anyone that could bring me more clarity on this topic.

Cedric