Thanks again, guys, for all your good thoughts!
I am planning to make some example recordings of the noise for you to hear exactly what it sounds like. Unfortunately only when I tried to connect my FA-101 to my new computer I realized my new computer doesn't have firewire, thus I couldn't connect the FA-101. Now I ordered a USB device instead and expect it in the mail today, so possibly the weekend will allow me to finally get some sound bits together for you.
I also had a simple Behringer UC6102 Guitar interface lying around and did some testing with it during the last days.
What I can say so far is this:
I go directly from the DS-5R to the recording input. (Bradley, can I connect headphones to the DS-5R?)
The noise is audible there already, although I must admit it is less annoying to me now than how I remembered it from the last time I tested it. It probably grew in my memory over time. But it is there nevertheless. Dead silent is not what I would call it.
The noise (hiss, hum, whatever) is non-directional. It is present even without the bass connected to the DS-5R. I guess that's an important insight because it should eliminate the possibility of the bass and the cable being the source.
What Jimmy says is what I thought too: It could also simply be a ground disagreement between his Alembic PSU... and, well, maybe not necessarily with my computer because the noise is present even when connecting to an amp instead of the computer, if I remember correctly. I sold my power amp therefore I can't test it right now.
I'll keep you posted when I recorded my example sound clips.
Thanks to you all!
Hartmut