4.16: Selecting the Optimal Filter

At the end of the previous section, a script generated this table of signal, noise, and SNR values for applying several different filter combinations to the N400 experiment.

Bandpass=0.1-10.0: Signal=-7.85, Noise=2.01, SNR=3.90
Bandpass=0.1-20.0: Signal=-7.93, Noise=2.02, SNR=3.92
Bandpass=0.1-30.0: Signal=-7.94, Noise=2.03, SNR=3.91
Bandpass=0.1-40.0: Signal=-7.96, Noise=2.03, SNR=3.91
Bandpass=0.5-10.0: Signal=-5.61, Noise=1.40, SNR=3.99
Bandpass=0.5-20.0: Signal=-5.69, Noise=1.43, SNR=3.99
Bandpass=0.5-30.0: Signal=-5.71, Noise=1.43, SNR=3.98
Bandpass=0.5-40.0: Signal=-5.72, Noise=1.44, SNR=3.98
Bandpass=1.0-10.0: Signal=-3.69, Noise=0.92, SNR=3.99
Bandpass=1.0-20.0: Signal=-3.77, Noise=0.96, SNR=3.92
Bandpass=1.0-30.0: Signal=-3.76, Noise=0.97, SNR=3.88
Bandpass=1.0-40.0: Signal=-3.79, Noise=0.97, SNR=3.90
Bandpass=2.0-10.0: Signal=-1.78, Noise=0.46, SNR=3.85
Bandpass=2.0-20.0: Signal=-1.80, Noise=0.50, SNR=3.59
Bandpass=2.0-30.0: Signal=-1.80, Noise=0.51, SNR=3.50
Bandpass=2.0-40.0: Signal=-1.84, Noise=0.52, SNR=3.54

That’s a lot of numbers, so I converted the values into a bar graph (Figure 4.13).

As you can see, the cutoff frequency of the low-pass filter (ranging from 10-40 Hz) didn’t have much impact on either the signal (panel A) or the noise (panel B). That’s because we measured the mean amplitude over a 200-ms time window. The uppies and downies of high-frequency noise largely cancel out over this time window. Low-pass filtering has a much bigger impact on scores like peak amplitude and peak latency. 

However, the high-pass cutoff had a large effect: As the high-pass cutoff increased, both the signal and the noise decreased. The signal decreased because the N400 contains a lot of low-frequency information, and filtering out more of this information (by increasing the high-pass cutoff) reduced the size of the N400. The noise decreased because there was a lot of low-frequency noise in the data, and this noise decreased more and more as the high-pass cutoff was increased.

The reduction in signal and the reduction in noise were approximately equal in most cases, so the SNR (panel C) did not change much as the high-pass cutoff increased. The exception was the 2 Hz cutoff, which reduced the signal more than it reduced the noise, causing the SNR to decrease. The best overall SNR came from a high-pass cutoff of 0.5 Hz (and the different low-pass cutoffs produced nearly identical SNR values with this high-pass cutoff).

From these results, you might think that a 0.5 high-pass cutoff would be ideal for the N400. However, we also need to take into account the waveform distortion produced by the filters. As we saw in Section 4.14, a high-pass cutoff of 0.5 Hz or higher led to unacceptably high levels of waveform distortion for the N400 (APP > 5%). 

Consequently, we can really only consider the filters with a high-pass cutoff of 0.1 Hz. Fortunately, the SNR for a 0.1 Hz high-pass filter was only slightly lower than the SNR for a 0.5 Hz high-pass filter. Thus, the 0.1 Hz cutoff gives us an SNR that is very high without producing any meaningful waveform distortion. It doesn’t really matter what low-pass cutoff we use (as long as we are scoring mean amplitude).

In our paper on the optimal filter settings for the ERP CORE paradigms (Zhang et al., 2024b), we did a more fine-grained exploration of the different possible cutoff values, and we found that a high-pass cutoff of 0.2 Hz was optimal for the N400. It produced a slightly better SNR than the 0.1 Hz cutoff while still producing minimal waveform distortion. This 0.2 Hz cutoff was ideal whether we were scoring mean amplitude, peak amplitude, peak latency, or 50% area latency.

For mean amplitude, we found that the 0.2 Hz high-pass cutoff could be combined with any low-pass cutoff of 10 Hz or higher. For peak amplitude, we found that a low-pass cutoff at 10 Hz was helpful when scoring peak amplitude (especially with noisy data), and a low-pass cutoff at 5-10 Hz was helpful when scoring peak latency or 50% area latency.

You have now seen all the steps needed to determine the optimal filter settings for a given dataset. This means that you can now determine the optimal filters for your own data. The process takes a long time if you do it using the eStudio GUI, but it’s pretty quick if you do it with a script. If you know a little about Matlab scripting, it should be straightforward for you to modify the scripts I have provided so they can be used with your own data.

Just imagine how impressed reviewers of your papers will be when they read your Methods section and find that you have rigorously determined the optimal filter settings for your data!

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