It could depend on context - are you speaking about the ability to separate these two things, or a specific instance of doing so?
'Signal' is a countable noun, so it needs an article if it is not plural. Although 'noise' can be non-countable, it should have a definite article in your example because it is specific noise that is being separated from the signal. You couldn't isolate and separate something from an abstract concept.
If you were talking about separating these two things in general, you should say:
You can separate signals from noise.
'Signals' is always countable, so it is a plural; noise can remain abstract because it is only possible that there may be noise.
If you are talking about a specific instance of this action, you should say:
You can separate the signal from the noise.
The definite article is appropriate as they are looking for a specific signal. If we are talking about radio signals, there are lots of signals everywhere, transmitted from all different places and on different frequencies. To receive or hear one, we have to isolate it, so you can see why they are countable.
I don't accept suggestions in other answers and comments that 'signal' can be non-countable, at least not in English grammar. Perhaps it is used that way as technical jargon in the field of radio communication, but if so, the majority of English speakers that do not work in that field may not recognise it. Many fields have their own terminology and it does not necessarily follow the rules of grammar. In my field of work, some English words are re-appropriated to mean something entirely different to their dictionary definitions.
Even if some related concepts can be non-countable - such as 'noise' and 'sound' - these are not the same as a 'signal'. Signals may be sent via mediums that are abstract, but that doesn't make them non-countable. It could be likened to the difference between 'a letter' and 'mail'. 'Mail' is non-countable and can refer to a single piece of correspondence, many pieces, all pieces, or the concept of sending correspondence. 'Letter' is always countable, even though you send letters through the mail.
As for which goes first... if 'sift' is actually the correct term for separating a signal from noise, then it doesn't really matter which goes first. Sifting is used to separate things. But it seems reasonable to keep 'signal' in first place as that is thing you want to keep. But it doesn't sound idiomatic to me.
I have some experience in audio production and the term I would use is filter. When you filter something, you remove it. So I would say I was filtering the thing I want to remove from the thing I want to keep, for example:
Filter out the noise from the signal.