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fourier transform homework

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tau17

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hi
this is a question from a book but it seems a strange one it says for the following prove that the inverse fourier transform is complex and the real n imaginary parts are a hilbert pair.

a) G(f)=1/2 at f=0
b) G(f)=0 for f<0


the way i see it it is 1/2delta(f) at f=0 and that should inverse transform to 1/2 and that is real or am i supposed to take it as 1/2+0j and take fourier transform of 1/2 that is half delta and that multiplied by -jsgn(f) would lose the dc value so its inverse would be 0 as hilbert removes dc component
and i dunno what to do about (b)
can some one please help
 
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