Hilbert Transform of signals

Q7. In Hilbert transform of a signal, the phase angles of all components of a given signal are shifted by

Options:

a) a) +/- π
b) b) +/- π/4
c) c) +/- π/2
d) d) Any angle from 00 to 3600

Correct Answer: c) +/- π/2

Explanation :

The Hilbert Transform g’(t) of the signal g(t) is defined by
g’(t) = (1/π)(τ)/(t - τ)d(τ), -∞ to + ∞
Hilbert transform may be obtained by first taking the Fourier Transform of the signal g(t), multiplying it by –jsgn(f), then taking the inverse Fourier Transform and therefore obtaining g’(t). –jsgn(f) is –j for the positive frequency f, and therefore the Hilbert Transform shifts the signal by -900 for a linear system whose input is g(t) and output obtained is g’(t).