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Hilbert transform filter phase

  1. Jun 19, 2011 #1
    We know that hilbert transform is a linear filter whose frequency response is given as -j*sgn(f), where f is the baseband frequency. Hence magnitude response of this filter is 1 and phase response is -pi/2 for f > 0 and pi/2 for f < 0. Hence phase response curve is like a staircase function ( with a shift of pi at f = 0)

    Now, my doubt is can a filter whose phase response is s.t there a phase shift of pi radians at f = 0. but it increases linearly and continuously from (-inf, 0) and (0, inf) be used as a hilbert transform filter? (assuming mag response is equal to one).
  2. jcsd
  3. Jun 20, 2011 #2


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    Science Advisor

    A linear phase shift is a constant time delay, not a constant phase delay as required.
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