# Firfilt FAQ

### Q. What are passband, stopband, transition band width, cutoff frequency, passband ripple/ringing, and stopband ripple/attenuation?

A. You can find explanations in this file(pdf) created by Andreas Widmann.

### Q. What is the difference between the “Basic FIR filter (legacy)” and the “Basic FIR filter (new)”? Which should I use?

A. The heuristic for automatically determining the filter length in the legacy basic FIR filter (pop_eegfilt) was inappropriate (possibly causing suboptimal filtering or unexpected filter effects). The new basic FIR filter (pop_eegfiltnew) has a new heuristic for automatically determining the filter length and is based on the firfilt plugin. The legacy function should only be used for backward compatibility purposes.

### Q. What is the difference between the “Basic FIR filter (new)” and the “Windowed sinc FIR filter”?

A. Both are based on windowed sinc filters. The basic filter applies a hardcoded hamming window, has an automatic default for filter length, and is defined by the passband edges. The windowed sinc FIR filter allows manual selection of window type, estimation of filter length by transition band width (no default), and is defined by cutoff frequencies (-6dB, half amplitude).

### Q. Why does firfilt-plugin run faster than the legacy EEGLAB filter?

A. The firfilt plugin does not use filtfilt to achieve zero-phase but shifts the signal by the filter’s group delay (NB: requiring ODD filter length/even filter order). So, the data are only filtered once with multi-threading (filtfilt does not seem to be multi-threading capable).

### Q. What is the recommended passband ripple/stopband attenuation/window type?

A. Ripple, i.e. deviation from the requested frequency response (0 in stopband, 1 in passband) is equal in passband and stopband in windowed sinc FIR filters. Ripple/attenuation is defined by the window type. 0.002 to 0.001 (that is, 0.2 to 0.1%; Hamming or Kaiser window) are reasonable starting values. This equals a stopband attenuation of -53 to -60 dB which is ok.

### Q. Should we prefer separate high- and lowpass filters over bandpass filters?

A. With separate hidh- and lowpass filter transition band width can be defined independently. Highpass filter often require narrower transition bands than lowpass filters. Separate filtering is preferable in these cases.

### Q. What is the difference between filter length and filter order?

A. Filter order is defined as filter length minus 1.

### Q. What is the transition band?

A. The transition band is the frequency band/range between the passband edge and the stopband edge. In windowed sinc FIR filters the -6dB cutoff is in center of the transition band.

### Q. What is the slope of windowed sinc FIR filters in dB/oct (as in IIR filters)?

A. Slope CANNOT be defined in dB/oct for windowed sinc FIR filters. Rather use transition band width. There is no straightforward conversion of slope in dB/oct to transition band width due to conceptual differences between FIR and IIR filters. IIR filters do not have a defined stop band.

### Q. What is the lower limit for cutoff frequency for high-pass filter?

A. There is no theoretical lower limit, however, the lower the cutoff the steeper is the roll-off and the higher is the filter order (length). Very low cutoff frequencies as low as 0.01 Hz as sometimes found in the literature require extremely long filters (FIR) or are prone to instability (IIR). To our experience a lower limit of about 0.1 Hz is recommendable for FIR filters. For lower cutoff frequencies consider IIR filters combined with a reduced sampling frequency of the signal.

### Q. What is the recommended transition band width (for a windowed sinc FIR highpass filter)?

A. Generally, the slope in the frequency domain should be as low/flat as possible, that is the transition band as wide as possible. Steeper slopes reduce the precision in the time domain; distortions and artifacts are additionally spread wider due to the longer filter length. A good staring value for a highpass filter: twice the cutoff frequency (-6 dB) for cutoff <= 1 Hz, 2 Hz for cutoff frequency < 1 and <= 8 Hz and 25% of cutoff frequency for cutoff > 8 Hz. This is also the heuristic implemented in the new basic FIR filter (generalized for all critical frequencies). However, please note, that it is recommended to (manually) adjust this heuristic to the application of interest. Do not go beyond twice of the cutoff frequency (i.e., transition band goes below DC/0 Hz). TIP: Strong attenuation (<< -60dB) can be important for DC/0 Hz (e,g,, to get rid of the DC offset for Biosemi files or to avoid baseline correction). By using twice of the cutoff frequency for transition band width, a type 1 windowed sinc filter can be tuned for excellent DC attenuation.

### Q. What stopband attenuation is good?

A. The community default of Hamming window/-53dB is a good starting value. With Kaiser windows stopband attenuation can be precisely adjusted.

### Q. How can I find optimal values for cutoff frequencies, attenuation, and filter length for my particular application?

A. By testing and systematically comparing the effects of different filters on the signal in the time domain.

### Q. Where can I read more about windowed sinc FIR filters?

A. Check out Engineers guide to digital signal processing.

### Q. For Granger Causality analysis, what filter should be used? (04/26/2018 Updated)

A. There are a few important things to confirm.

- Barnett and Seth (2011) showed that multivariate Granger causality is in theory invariant under zero-phase (a.k.a. phase-invariant) filter. They do recommend filtering to achieve stationarity (e.g., drift, line noise) See Seth, Barrett, Bernett (2015).
- However, in practice, filtering causes problems in calculating multivariate Granger causality. The main problem is the increase in model order. This is because filtering makes the power spectrum density of the signal complicated (low power in the stopband, steep roll-off, etc). See the following example: 33ch EEG, downsampled to 100 Hz, without (top) and with (bottom) applying 44.5Hz low-pass filter (FIR, Blackman, TBW 1 Hz). Notice that the estimated model orders is worsened from 10 (without LPF) to 14 (with LPF)--but apparently taking 16 (with LPF) is the right decision here from AIC, FPE and HQ results.

- The second problem, which comes from the same reason mentioned above, is that empirical estimates of VAR parameters yields unstable models due to poor parameter estimate for increased model order.
- The third problem is that filtering causes numerical instabilities in estimating causality.

How can we address these problems?

- When applying a high-pass filter to achieve stationarity, let the transition band end at DC (i.e. 0Hz). For example, when you use EEGLAB's 'Basic FIR filter (new, default)‘ to apply high-pass filter with 'passband edge' below 2-Hz, the transition band is automatically adjusted so that it always ends at DC. (We use 1-Hz highpass for the ICA purpose; empirical test is required to see whether 2-Hz highpass is beneficial for GCA compared with 1-Hz). If you want to set the high-pass filter passband edge above 2 Hz, we recommend you use 'Windowed sinc FIR filter' to design the filter so that it has the stopband at DC. (CAUTION: 'Windowed sinc FIR filter' uses
**cutoff frequency**and not**passband edge**i.e. cutoff frequency of 1 Hz is equivalent to passband edge at 2 Hz; See Q3) - When treating the line noise, use CleanLine() instead of notch filter because the former is phase-invariant.
- When downsampling data (which is useful for multivariate Granger causality analysis), use mild anti-aliasing filter and do not let the stopband below the Nyquist frequency. In practice, use the following example.

EEG = pop_resample(EEG, 200, 0.8, 0.4);

In this example, you are downsampling your data to 200Hz, with cutoff frequency being 160Hz (i.e. 200Hz*0.8) and the transient bandwidth 80Hz (i.e. 200Hz*0.4).

### References and recommended readings

- Duncan-Johnson, C. C., & Donchin, E. (1979). The time constant in P300 recording. Psychophysiology, 16, 53–56.

- Barnett, L., & Seth, A. K. (2011). Behaviour of Granger causality under filtering: theoretical invariance and practical application.J Neurosci Methods. 201, 404-419.

- Van Rullen, R. (2011). Four common conceptual fallacies in mapping the time course of recognition. Frontiers in Psychology, 2, 365. doi: 10.3389/fpsyg.2011.00365

- Acunzo, D. J., MacKenzie, G., & van Rossum, M. C. W. (2012). Systematic biases in early ERP and ERF components as a result of high-pass filtering. Journal of Neuroscience Methods, 209, 212–218. doi: 10.1016/j.jneumeth.2012.06.011

- Rousselet GA (2012) Does filtering preclude us from studying ERP time-courses? Front. Psychology 3:131. doi: 10.3389/fpsyg.2012.00131

- Widmann, A., & Schröger, E. (2012). Filter effects and filter artifacts in the analysis of electrophysiological data. Frontiers in Psychology, 3, 233. doi: 10.3389/fpsyg.2012.00233

- Zoefel, B., & Heil P. (2013). Detection of near-threshold sounds is independent of EEG phase in common frequency bands. Front Psychol, 4, 262.

- Luck, S. J. (2014). An introduction to the event-related potential technique (2nd ed.). Cambridge, MA: MIT Press.

- Widmann, A., Schröger, E., & Maess, B. (2015). Digital filter design for electrophysiological data--a practical approach. J Neurosci Methods, 250, 34-46. doi: 10.1016/j.jneumeth.2014.08.002 link

- Tanner, D., Morgan-Short, K., & Luck, S. J. (2015). How inappropriate high-pass filters can produce artifactual effects and incorrect conclusions in ERP studies of language and cognition. Psychophysiology, 52(8), 997-1009. doi: 10.1111/psyp.12437

- Seth, A. K., Barrett, A. B., & Barnett, L. (2015). Granger causality analysis in neuroscience and neuroimaging. J Neurosci. 35, 3293-3297.

- Maess B, Schröger E, Widmann A. (2016). High-pass filters and baseline correction in M/EEG analysis. Commentary on: "How inappropriate high-pass filters can produce artefacts and incorrect conclusions in ERP studies of language and cognition". J Neurosci Methods. [Epub ahead of print]

- Tanner D, Norton JJ, Morgan-Short K, Luck SJ. (2016). On high-pass filter artifacts (they're real) and baseline correction (it's a good idea) in ERP/ERMF analysis. J Neurosci Methods. [Epub ahead of print]

- Maess B, Schröger E, Widmann A. (2016). High-pass filters and baseline correction in M/EEG analysis-continued discussion. J Neurosci Methods. [Epub ahead of print]

- Liljander S, Holm A, Keski-Säntti P, Partanen JV. (2016). Optimal digital filters for analyzing the mid-latency auditory P50 event-related potential in patients with Alzheimer's disease. J Neurosci Methods. 2016 Mar 22;266:50-67.

(This page was created by Makoto Miyakoshi and Andreas Widmann.)