Time-series EEG Resampling to Fix Poor Voltage Resolution?

Question

I’ve made quite a bad mistake in ca. 14 EEG recordings – I recorded at 10uV resolution @ 5000 Hz instead of 0.1 uV @ 500 Hz. I’m conducting an ERP experiment, and the signals of interest are on the order of ~5 uV. I’m wondering if there is any way to up-sample the voltage given I have way more time series data points than I need..? Some sort of interpolation?

I’ve seen a number of posts on up-sampling from say 500 hz to 1000 hz, but not sure if the principal is the same?

This represents about 42 hours of recording time and I’m anxious to know if I can recover any usable data from these recordings, or if I have to try to get participants back in (there is a treatment enrollment deadline which means I can’t simply acquire more data). Thanks very much,

pk

Answer 1

A way how to increase the resolution of your signal is to use signal averaging. That means you apply a sliding window filter. In your case, this would be a filter of length 10 since your signal is oversampled by a factor of 10. You can't use a longer filter than of length 10 because you actually might filter out information you are interested in. Now, here is the catch. Whatever improvement this averaging is going to give you (depending on if the noise is zero mean Gaussian distributed or not) won't be enough to get you to your desired resolution of 0.1V. In my opinion you will need to redo the experiment. Here is a post you might find interesting https://dsp.stackexchange.com/questions/48205/why-does-signal-averaging-reduces-noise-levels-by-more-than-sqrtn?rq=1

Answer 2

You will have to redo the experiments.

Though you do have sufficient temporal resolution, this will in no way help to increase you voltage resolution. Since the recording equipment performs analog to digital conversion quantization with the specified resolution, meaning you will have an uncertainty of half your resolution (10uV/2 = 5 uV). This is in range of the signals that you want to measure, so the signal you want to see will maybe jump across a couple different levels (perhaps 2 based on the info you provide).