Which one of the following is the correct Fourier transform

Which one of the following is the correct Fourier transform of the unit step signal?

We know that

u(t) =	1	[1 + sgn(t)]
	2

The Fourier transform is given by

F{u(t)} =	1	[F{1} + F{sgn(t)}]
	2

=	1		πδ(ω) +	1
	2			jω

= πδ(ω) +	1
	jω

Hence, alternative (C) is the correct choice.

	1	+ 2πδ(ω)
	jω