4.3: Exercise- Assessing the Frequency Content of the Noise

We’re going to start by thinking about filtering as a frequency-domain operation, in which we suppress some frequencies and pass others. If you don’t already know the basics of Fourier analysis and how filtering works in the frequency domain, I recommend that you stop and learn those basics before going through the rest of this chapter. A quick way to learn those basics is to watch the videos for Part 1 and Part 2 from Chapter 6 of my free online Introduction to ERPs course. Each of the videos is only about 5 minutes long, so they'll get you up to speed quickly.

To start fresh, click the Reset button under the lower right corner of the plot region and then click Reset ERPLAB Studio in the window that appears. Set Chapter_4 to be Matlab’s current folder. Go to the ERP tab in eStudio and use the Load button in the ERPsets panel to load the ERPset file named waveforms.erp. It should look something like Screenshot 4.1.

The first channel shows an artificial waveform that I created in Excel. The second channel is the sum of the first channel and a 60 Hz sine wave (like the line noise that is often picked up from electrical devices in the recording environment).

Line Noise

AC electrical lines run at 60 Hz in North America and some other parts of the world. Europe, China, India, and some other regions use 50 Hz. We often call this the line frequency to be agnostic about whether it is 50 or 60 Hz. The noise produced by this signal is called line noise.

Before we filter the data, let’s perform a Fourier transform on these waveforms so that we can see their frequency content. Go to the Spectral Analysis panel, make sure it's set up as shown in Screenshot 4.2, and then click the Plot button.

You should see something like the spectral plot in Screenshot 4.3. The X axis is the frequency, and the Y axis is the amplitude at this frequency. This plot tells us that we could reconstruct the original time-domain waveform by summing together a set of sinusoids with the set of amplitudes shown at each frequency in the plot. We’d also need to know the phase at each frequency to reconstruct the original waveform, but phase information isn’t usually shown with ERP data. You can get a quick introduction to the Fourier transform in Chapter 6 of my online Introduction to ERPs course (or just watch this YouTube video). You can find a more detailed treatment in Chapters 7 and 12 of Luck (2014).

As you can see from the amplitude spectrum, the original ERP waveform mostly consists of relatively low frequencies. This is fairly typical of the waveforms you would see in most perceptual, cognitive, and affective experiments. In low-level sensory experiments, you might see more high-frequency activity.

The amplitude spectrum for waveform+60Hz is just like the amplitude spectrum for the original waveform, except that there is also activity around 60 Hz. This is because I created that ERP waveform by summing together the original waveform and a 60 Hz waveform. Note that the peak amplitude around 60 Hz is approximately 0.05 µV. That will become relevant in the next exercise, where we will apply a filter to reduce the amount of 60 Hz noise.

When you’re first starting out in ERP research, you should plot Fourier transforms like these prior to filtering so that you have a good idea of the frequency content of the noise in your data. This can help you figure out where the noise is coming from (because different sources of noise have different frequency content). By knowing where the noise is coming from, you may be able to eliminate it in future recordings. It’s better to reduce the noise before it contaminates your data rather than relying on filters and other signal processing techniques. For reasons described in Luck (2014), I call this Hansen’s Axiom: “There is no substitute for clean data.” As we will see later in this chapter, filters reduce the temporal precision of your data. And isn’t temporal precision one of the most important features of the ERP technique?

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