1. Square waves also work. That's the Hadamard transform.
2. Individual neurons produce very short spikes (action potentials). EEGs measure those spikes in aggregate, which creates a very noisy and not at all sinusoidal signal. The Greek letters denote particular frequency bands, so if a graph of "alpha waves" looks somewhat sinusoidal, it's because the signal has been filtered to suppress other frequencies.
1. Can I ask where you learned that? So happy to know this. By virtue of the 0/1 approach, it seems almost more fundamental than sine waves. Or, maybe negative infinity to infinity is more fundamental? Anyhow, that's just metaphysics. I'm also curious what it implies for digital computing
Here is a nice article that taught better than Wikipedia: https://www.mathworks.com/help/signal/ug/walshhadamard-trans...
2. Alpha on a single EEG channel can look pretty sinusoidal. Is there a measure of sinusoidality that would allow me to assert how sinusoidal they are?
2. Individual neurons produce very short spikes (action potentials). EEGs measure those spikes in aggregate, which creates a very noisy and not at all sinusoidal signal. The Greek letters denote particular frequency bands, so if a graph of "alpha waves" looks somewhat sinusoidal, it's because the signal has been filtered to suppress other frequencies.