Hilbert transform is used to transfer signal into analytical signal. But why after the transform, the envelop and instant frequency (if the signal is monogenic) can be calculated. What is happened in the transform? What is the relationship between these two signals?
BTW, according to wiki page analytic signal is
In mathematics and signal processing, a signal which has no negative-frequency components is called an analytic signal
why to use Hilbert transform, instead of Fourier transform to calculate analytical signal? Is there a special reason to do so?