One important thing about the hilbert transform is that it is noncausal, and so in practice for realtime applications can only be approximated, and the better t

One important thing about the hilbert transform is that it is noncausal, and so in practice for realtime applications can only be approximated, and the better the approximation the larger the delay imposed by the need for newer parts of the signal to compute older results. For at lot of applications this doesn't matter, but it does make it harder to use.