You don't really need a DSA for this task. DSA's have two discrete measurement channels phase-locked to the generator for transfer function analysis/FRA. With their added complexity, these units tend to be large, heavy, and loud (fans).
Any of the single-channel FFT analyzers from the 80's on that have selectable DC-coupled input will do the trick.
Ono Sokki made some reasonably-sized ones and were well-built. Size-wise the HP 3561A isn't too bad. There were some smaller units from Nicolet, Spectral Dynamics, AND aka A&D aka Zonic, and others, often marketed as "mini-FFT", "personal-FFT", and the like.