Wavelet Transfrom + Power Spectral Density (using Matlab)
You need to do 1-Dimensional wavelet package decomposition. Here is the matlab documentation for the command to do this.

Here is some example code based on what you've described above:

wpt = wpdec(X, 2, 'db1', 'shannon')
plot(wpt)


This will provide a nice clickable graph. As you'll see in the documentation, you can provide a lot of different parameters for the decomposition.