Only thing that you can easily determine from the frequency spectrum analysis is what is the sampling frequency of the input mp3 file.
For example, if your mp3 is sampled at 44100, you won't have any sound above 22050hz and that will be clearly visible on the spectrum graph.
Since you are crossing into transcendental domain here, try this:
- encode mp3 to 128kbps
- transcode it to say 320kbps
- try RAR-ing or 7Z-ing resulting file and original file. Observe compression ratios.
Their 'entropy' ie. randomness will differ, and maybe that number will tell you something about how much information is 'fabricated' in bitrate expansion during transcoding.