5.3: Exercise- Working with the Artificial Data
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In the Chapter_5 data folder, you will find an Excel spreadsheet named simulated_data.xlsx , which contains everything I used to create the simulated data in Figure 5.1. Open the file in Excel (or import it into Google Sheets). You will see that each line is a time point. The first column shows the latency of the time point (in ms), and the second column is the source waveform. There are also columns for the absolute voltage at each electrode site, with the weighting factor for a given site in the second row.
If you look at the equations in the cells that compute the absolute voltage values, you’ll see that the absolute voltage at a given electrode site was computed by multiplying the weighting factor for that site by the source waveform. You’ll also see that the single-ended voltage was created by subtracting the absolute voltage at the ground electrode from the absolute voltage at each other site, and then adding the 60 Hz noise. And you’ll see that the referenced voltage was computed by subtracting the single-ended signal at the Lm electrode from the single-ended signal at a given active site. At the right side of the spreadsheet, you’ll see plots of the absolute voltages, the single-ended voltages, and the referenced voltages. Take a careful look at the equations in the spreadsheet and make sure that you understand how the absolute voltage is related to the source waveform and the weights, how the single-ended voltage is related to the absolute voltage, and how the referenced voltage is related to the single-ended voltage.
The spreadsheet also contains sheets with copies of the data formatted for exporting as a text file (using the Tab delimited Text format), which can easily be imported into ERPLAB (using EEGLAB > ERPLAB > Export & Import ERP > Import ERP from text (universal) ). This allows you to create simulated data and see how the various ERPLAB processes work.
In the spreadsheet, change the weight above the Absolute_Ground label from -.04 to -.10 . You’ll see that this greatly increases the magnitude of the absolute voltage in the ground channel. And because the ground is subtracted from the other signals to create the single-ended voltage, this also changes all the single-ended voltage waveforms. But did it change the referenced waveforms?
No, it did not! The nature of the referencing procedure means that any signals or noise at the ground electrode are subtracted away from the referenced voltages. This means that you can place the ground electrode anywhere on the head, and the location does not matter. You might then wonder why we use a ground electrode at all. The answer is simple: The amplifier will freak out if there isn’t a ground electrode. You need to have a ground, and it needs to be appropriately attached to the head (or anywhere on the body). But the location does not matter.
Now try changing the weight for the Lm channel from -.011 to -.20 . This simulates changing the location of the reference electrode, moving it farther away from the zero line. What did this do to the referenced waveforms? Not only are some of them now larger, the polarity of the Fz waveform has now changed from negative to positive. This demonstrates how the signal at the reference electrode can have a large impact on the referenced waveforms from the so-called active electrodes.
Play around with the spreadsheet some more. For example, try changing the weights for the other electrodes or the magnitude of the 60 Hz noise.