If an arbitrary "signal" at an arbitrary frequency was received at Earth, would there be any way to tell if it was redshifted?

Question

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.

Answer 1

Naturally physicists would try to get a signal for comparison from a source with different speed by e.g. satellites. Also there would be some guesses what the original frequency was. If the signal is continuing for a longer time, we can use earth motion around the sun if the signal comes from outside the solar system and even triangulate it if it is not too far away.

But if the signal uses a frequency which is not expected so we have only one receiver and the signal stops after a short time, we are out of luck. Without a comparison we cannot determine the source frequency.