Learning Objectives
In this chapter, you will learn to:
-
Compare the frequency content of an ERP waveform with the frequency response function of a filter to predict how well the filter will attenuate the noise in the data
-
Determine the
impulse response function
of a filter and conceptualize filtering as a process that replaces each point in the unfiltered waveform with a scaled copy of this function
-
Think of an ERP waveform as a series of
impulses
, one at each time point
-
Predict how a filter will distort an ERP waveform on the basis of the filter’s impulse response function
-
Select filter parameters that provide the best balance between noise reduction and distortion of the waveform
-
Create artificial waveforms and filter them to see how a filter might be distorting your data
You
must
use filters in ERP experiments. At a minimum, your amplifier includes an
antialiasing
filter that must be used prior to digitizing the EEG. In almost all ERP experiments, additional filtering is important for reducing sources of noise that would otherwise create large measurement error and reduce your statistical power. However, when filters are misused, they can dramatically distort your data, leading to incorrect conclusions. As a result, it’s vitally important that you understand how filters work and the conditions under which they can produce significant distortion of your ERP waveforms.
For most ERP researchers, there is no topic more boring than filtering. At the core of filtering is a mathematical operation called
convolution
. Even the word “convolution” sounds complicated and boring!
However, you can get a reasonable understanding of filtering by seeing how convolution works visually, without ever seeing an equation. This chapter takes you through a set of exercises that will show you how convolutions are used for filtering without any equations. If you want a more detailed description of filtering, you should read Chapter 7 in Luck (2014). If you want to understand the math, you can read Chapter 12 in Luck (2014), which is
available for free online
.