Hilbert Transform of signals
Q. In Hilbert transform of a signal, the phase angles of all components of a given signal are shifted by- Published on 15 Oct 15a. +/- π
b. +/- π/4
c. +/- π/2
d. Any angle from 00 to 3600
ANSWER: +/- π/2
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).
