I've been thinking a lot about SETI and aliens, and, just for fun (layman), learning a lot about redshift: why it's possible despite $c$ being constant, how we know stars are red- or blueshifted. But I've yet to find an answer to this idea:
Given an arbitrary signal (say a burst of x-ray, radio, infrared light, whatever) for which we have no context or information (i.e. it doesn't appear to be coming from a star or some other obvious astronomical, documented source), is there a way to tell whether the transmitter is approaching us?
In other words, if aliens blast us with music encoded in x-ray in an encoding/protocol we aren't expecting, is there any way to know if they're driving toward us or not?
My confusion arises from the fact that as I understand it, frequency can be red or blue shifted all the way out of a given spectrum. This may be incorrect, but since my understanding is that visible light can be redshifted to infrared, presumably then it could be shifted all the way to an x-ray frequency, if the relative velocity difference was large enough.