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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?

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  • $\begingroup$ Usually you calculate the Hilbert transform via Fourier transform with proper multiplication of negative frequencies. So anyway you are ending up with using some flavour of FFT routines and ending up with analytical signal, having nice properties. $\endgroup$ – jojek Dec 2 '14 at 8:43
  • $\begingroup$ @jojek Why does simply removing the negative frequencies provide these nice properties? $\endgroup$ – Kattern Dec 2 '14 at 9:08

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