Specifically the discrete wavelet transform. Even more specifically, how to determine the frequency bands that result from the samples and how to calculate the power in that band.
I have some EEG data. I load it up in Matlab in the wavelet toolbox using their GUI, and do the discrete wavelet transform. I have arbitrarily picked the daubechie5 wavelet. From my understanding, since my signal was originally sampled at 500 Hz, the first level transform breaks it into 0-250 Hz, and 250-500 Hz. The lower 0-250 Hz is the so-called approximation, and the 250-500 Hz is the details. Fine. Then the second level would break the approximation into two again, and so on and so on until after 5 levels I have 5 sets of detail coefficients and 1 set of approximation coefficients. From these I can reconstruct the waveform.
In theory, or at least in my head, if I’m interested in the 61-125 Hz range, I can take detail set 3 (set 1 being 250-500, 2 = 125 - 250, 3 = 61-125) and the final approximation and reconstruct the signal from just that and I should get the time-scale-amplitude for only that scale.
Here are my questions:
Is that breaking things in half correct? So if I wanted to see 125-250 Hz, I’d look at level 3?
How would I calculate the power in the signal in that frequency band assuming I’m correct on how to extract it?
I’m sure I’ll think of more, but after reading so many articles that assume I have some basic knowledge that I don’t have, I’m getting a bit lost.