Well, if your original signal is full of a large number of frequency components, the spectrum will be, too. This looks like a few dominants with a large number of what may be sidebands and harmonics/subharmonics. You might see what a dB scale (log) looks like instead of just linear.
What is the signal? Knowing something of the system might let somebody here expound at depth; ya' never knows, but there's a "veritable plethora" of backgrounds/experience.
One issue that could be a problem depending -- was the data collected with analog anti-aliasing filters or some other way to ensure sampling was fast enough to avoid aliasing? If there were components in the original signal higher than or very near the Nyquist, they will fold back into the computed frequency range. If that is the case, once the data are sampled, there's no way to remove that source of contamination.