4.14: Key Takeaways and References
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Key Takeaways
- You can filter EEG and ERPs in the frequency domain using the Fourier transform, or you can filter in the time domain using an impulse response function or a weighting function. These three approaches are mathematically identical and produce exactly the same result. However, we mainly care about the time domain in ERP research, so it’s helpful to think about filtering as a time-domain operation.
- The impulse response function of a filter is just the output of the filter when the input is an impulse of amplitude 1 at time zero.
- You can think of an ERP waveform as a sequence of impulses, one at each time point. The output of a filter for a given input waveform can be computed by replacing each impulse in the input waveform with a copy of the impulse response function that has been scaled by the amplitude of the impulse and then summing them together.
- You can also think of filtering as being implemented by a weighted running average. The weighting function is the mirror image of the impulse response function. This conceptualization allows you to see how the filtered value at a given time point is related to the values at the surrounding time points.
- Precision in the time domain is inversely related to precision in the frequency domain. The more heavily you filter, the more temporal distortion you will produce. The amount of temporal “smearing” produced by a filter is easily understood by the width of the impulse response function or weighting function. Heavy filtering can introduce artifactual peaks in your waveform, especially with high-pass filters or steep roll-offs, potentially causing you to draw completely bogus conclusions.
- For most perceptual, cognitive, and affective ERP experiments, filtering from 0.1 to 30 Hz works very well. If you want to filter more heavily, you should first apply the filter to artificial waveforms so that you can see what kind of distortion is produced by the filter.
References
Bae, G. Y., & Luck, S. J. (2018). Dissociable decoding of working memory and spatial attention from EEG oscillations and sustained potentials. The Journal of Neuroscience , 38 , 409–422. https://doi.org/10.1523/JNEUROSCI.2860-17.2017
Bigdely-Shamlo, N., Mullen, T., Kothe, C., Su, K.-M., & Robbins, K. A. (2015). The PREP pipeline: Standardized preprocessing for large-scale EEG analysis. Frontiers in Neuroinformatics , 9 . https://doi.org/10.3389/fninf.2015.00016
de Cheveigné, A. (2020). ZapLine: A simple and effective method to remove power line artifacts. NeuroImage, 207, 116356. https://doi.org/10.1016/j.neuroimage.2019.116356
Klug, M., & Kloosterman, N. A. (2022). Zapline-plus: A Zapline extension for automatic and adaptive removal of frequency-specific noise artifacts in M/EEG. Human Brain Mapping, 43(9) , 2743–2758. https://doi.org/10.1002/hbm.25832
Griffin, D. R., & Galambos, R. (1941). The sensory basis of obstacle avoidance by flying bats. Journal of Experimental Zoology , 86 , 481–506. https://doi.org/10.1002/jez.1400860310
Kappenman, E. S., & Luck, S. J. (2010). The effects of electrode impedance on data quality and statistical significance in ERP recordings. Psychophysiology , 47 , 888–904. https://doi.org/10.1111/j.1469-8986.2010.01009.x
Luck, S. J. (2005). An Introduction to the Event-Related Potential Technique . MIT Press.
Luck, S. J. (2014). An Introduction to the Event-Related Potential Technique, Second Edition . MIT Press.
Mitra, P. P., & Pesaran, B. (1999). Analysis of Dynamic Brain Imaging Data. Biophysical Journal , 76 (2), 691–708. https://doi.org/10.1016/S0006-3495(99)77236-X
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 , 997–1009. https://doi.org/10.1111/psyp.12437