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Which of the following is true regarding the frequency response of Hilbert transform?

Which of the following is true regarding the frequency response of Hilbert transform? Correct Answer Purely imaginary

Our choice of an anti-symmetric unit sample response is consistent with having a purely imaginary frequency response characteristic.

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Laplace transform of the function f(t) is given by $${\text{F}}\left( {\text{s}} \right) = {\text{L}}\left\{ {{\text{f}}\left( {\text{t}} \right)} \right\} = \int_0^\infty {{\text{f}}\left( {\text{t}} \right){{\text{e}}^{ - {\text{st}}}}{\text{dt}}{\text{.}}} $$       Laplace transform of the function shown below is given by
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