Extrapolation of band-limited frequency data

I’m now studying "How to do accurate transform from band-limited frequency data specifically S-parameter data of high speed interconnect to the causal impulse response in time domain. There are two known method, one is using rational fitting such as vector fitting of frequency data and the other is using IFFT of Hilbert transformed frequency data after the extrapolation of band-limited s-parameter data. I have read several paper which are related above thing, but I didn’t understand obvious concept for band-limited frequency data. I’ve seen a lot of text the band-limited frequency data makes a ringing such that non-causal impulse response. But I’ve not seen what is the definition of band-limited frequency data and when we say this frequency data is band-limited, what is the criterion of band-limited frequency data?

Anyone who knows explicit concept for band-limited frequency data, pleas explain.