Some properties are given below:
(i) A signal f (t) and its Hilbert f_h(t) have the same energy density spectrum.
(ii) A signal f (t) and its Hilbert transform f_h(t) have the same auto correlation function.
(iii) A signal f (t) and its Hilbert transform f_h(t) are mutually orthogonal i.e ∫^infin; _–∞ f(t) f_h(t) dt = 0
(iv) If f_h(t) is a Hilbert transform of f (t), then the Hilbert transform of f_h(t) is – f (t)
i.e. If H [f(t)] = f_h(t)
then H [f_h(t)] = – f (t)
The correct statements are—