Filter effects and filter artifacts in the analysis of electrophysiological data.

In a recent review, VanRullen (2011) concludes that electrophysiological data should not be filtered at all when one is interested in the temporal dynamics or onset latencies of the electrophysiological responses. This conclusion was based on the observation that response onset latency was “smeared out in time for several tens or even hundreds of milliseconds” (p. 6) in a simulated dataset.

It is correct that any band limitation in the frequency domain necessarily affects the signal in the time domain resulting in reduced precision and artifacts (cf. e.g., Luck, 2005). Nevertheless, here, we will discuss that the problem is overestimated by about an order of magnitude by the assumptions and analysis parameters used in VanRullen's simulated dataset and advertise the cautious usage of carefully designed filters to be able to also detect small signals.

Filter Selection

The filter selected in VanRullen's simulation was a bad choice as it results in artifacts not related to filtering per se. The FIR filter generated by EEGLAB (Delorme et al., 2011) with default settings exhibits excessive filter ringing (cf., Figure A1 in Appendix), and excessive pass-band ripple including non-unity gain at DC (the step response never returns to one). These artifacts are due to a known misconception in FIR filter design in EEGLAB. The artifacts are further amplified by filtering twice, forward and backward, to achieve zero-phase.

Figure A1

Prototypical low-pass linear-phase filters’ impulse, step, magnitude, and phase responses (top row; sampling frequency = 500 Hz, cutoff frequency 30 Hz). The EEGLAB “Basic FIR filter” (red, 49 points, default settings, EEGLAB v11.0.2.1b; Delorme et al., 2011) exhibiting excessive ringing artifacts (“ripples” in the time domain observed if filtering a non-oscillating input, e.g., a step signal, yields an oscillating output) is shown in comparison to a windowed sinc (green, 49 points, firfilt EEGLAB plugin; Widmann, 2006) and a discrete Gaussian kernel filter (σ = 6.18 ms, based on a modified Bessel function; Lindeberg, 1990). The minimum-phase converted version of the discrete Gaussian kernel filter (bottom row; “causal” filter converted by means of Hilbert transform) shows a considerably non-linear phase response but does not show a response before signal onset.

With more appropriate filters the underestimation of signal onset latency due to the smoothing effect of low-pass filtering could be narrowed down to about 4–12 ms in the simulated dataset (see Figure 1 and Appendix for a simulation), that is, about an order of magnitude smaller than assumed.

Figure 1

Impact of filter type and signal-to-noise ratio (SNR) on the time course of the averaged signal and the detected signal onset latency in the simulated dataset (sampling frequency 500 Hz; step signal; signal onset 150–180 ms) as defined by VanRullen (. The simulated dataset was filtered with the EEGLAB firls based filter, a windowed sinc FIR filter (Widmann, 2006), a discrete Gaussian kernel filter (Lindeberg, 1990), and a minimum-phase converted version of the Gaussian filter (causal; see Figure A1 in Appendix for a detailed description of the filters). Single trial signal-to-noise ratio was reduced in 20 dB-steps from +26 dB (original dataset; left column) to −14 dB (right column). The Gaussian filtered single trials (second row) and the averaged trials (third row) are displayed. Signal onset latency was measured by a running one-sided t-test (bottom row; gray bars) and jack-knifing with a relative 20%-criterion (black lines; Kiesel et al., 2008).

Signal-to Noise Ratio

The signal-to-noise ratio chosen by VanRullen for the simulated dataset is implausibly high (+26 dB at single trial level, +43 dB averaged) as signal-to-noise ratios smaller than one are common in real electrophysiological data. This assumption biases the conclusion on the detectability of the signal without filtering and overestimates the impact of filter ringing artifacts.

At more realistic signal-to-noise ratios no significant impact of the filter artifacts is observed (but only effects of transient smoothing by low-pass filtering; see Figure 1 and Appendix). The precision that can be achieved in the measurement of the response onset latency is limited by signal-to-noise ratio. Thus, the trade-off between filter effects versus the signal-to-noise ratio gain by filtering must be considered.

Filter Effects vs. Filter Artifacts

We also recommend to distinguish between filter effects, that is, the obligatory effects any filter with equivalent properties – cutoff frequency, roll-off, ripple, and attenuation – would have on the data (e.g., smoothing of transients as demonstrated by the filter's step response), and filter artifacts, that is, effects which can be minimized by selection of filter type and parameters (e.g., ringing).

Causal Filtering

In a commentary on VanRullen, Rousselet (2012) suggested to use “causal” filtering to solve the problem of signal onset latency underestimation due to smoothing. This is a valid recommendation, which has already been given (e.g., Luck, 2005). However, it should have been made explicit that the suggested type of “causal” filtering comes at the cost of a distortion of phase information also with FIR filters (cf., Figure A1 in Appendix).

The causality in filtering is not directly related to the symmetry of filter coefficients as implied in Figure 1 in Rousselet's (2012) comment. That is, the FIR filter labeled “non-causal” can also be applied in a causal way by not compensating the filter's delay (by not filtering the signal backward and not “left-shifting” the signal by the group delay). In order to reduce this filter delay in causal filtering, asymmetric “causal” FIR filters, more often referred to as minimum-phase filters, can be used. However, as FIR filter coefficients necessarily must be symmetric (or antisymmetric) for the filter to have linear-phase characteristic (Rabiner and Gold, 1975; Ifeachor and Jervis, 2002), 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. In its application it should be considered that the systematic delay and the non-linear phase response could also affect response onset information.

In the first paragraph of the appendix Rousselet (2012) suggests that the causal filtered signal could be left-shifted by the group delay to achieve zero-phase. We do not agree with this recommendation: First, this would re-introduce non-causality. Second, this statement is wrong as only linear-phase (anti-/symmetric FIR) filters can be made zero-phase by left-shifting the signal.

Conclusion

In the analysis of electrophysiological data signal-to-noise ratio has to be improved by all adequate means. Priority should be given to the collection of higher numbers of trials and reduction of noise in data recording. However, in most situations filtering will nevertheless be necessary to appropriately analyze electrophysiological data. In these situations it is essential to know and understand the effects of filtering on the data and cautiously adjust filter settings (cutoff frequencies, roll-off, attenuation, and ripple) to the signal of interest and the particular application, e.g., by evaluating the effects of different filters on the data. Especially the high-pass filtering of slow ERP components or blinks, as commonly observed in the literature, might seriously affect ERP time course and amplitudes (see, Luck, 2005, for a detailed discussion). Furthermore, we recommend not using default filter settings, in particular when using EEGLAB, but rather to manually and carefully select filter type and parameters to minimize filter artifacts.

Filtering can result in considerable distortions of the time course (and amplitude) of a signal as demonstrated by VanRullen (2011). Thus, filtering should not be used lightly. However, if effects of filtering are cautiously considered and filter artifacts are minimized, a valid interpretation of the temporal dynamics of filtered electrophysiological data is possible and signals missed otherwise can be detected with filtering.