[wglb]

But the point is that the transform shows you two representations, one time-based, the other frequency-based, of the same signal.

And notice that time is a component in each of these.

[zodiac]

It doesn't need to be time- and frequency- based. For example in quantum mechanics you transform from position to momentum space. I think the complaint was that the word "signal" excludes this later case while "function" is more general.