I am referring to the figurative expression (and not to its literal usage in electrical engineering).
Thanks for the context - it helps.
I would use "the" with both nouns as I also assume that the context includes made in an earlier reference to "what people are saying". iei.e. the signal, and "the various imperfect ways they are saying it", i.e. the noise.
Does signal always go before noise?
Usually, (usually does not mean "always") the thing you want is the first item, unless the following sentence or clause refers to the unwanted item.