The function x(t) is shown in the given figure. If X(jω)

The function x(t) is shown in the given figure. If X(jω) is the Fourier transform of the x(t), then |X(jω)| at ω = 0 will be—

Given waveform of x(t) is a combination of four shifted step function i.e.,

i.e., x(t) = u		t +	1		+ u		t +	1		- u		t -	1		-u (t - 1).......A
			2					2					2

F[x(t)] =	e^jω	+	e^jω/2	−	e^−jω/2	−	e^−jω
	jω		jω		jω		jω

X(jω) =		e^{jω − jω/2}		+		e^jω/2 − e ^jω/2
		jω				jω

X(jω) =	2	sin ω +	2	sin	ω
	ω		ω		2

\|X(jω)\|_{at ω = 0} = lim_{ω → 0}		2	sin ω +	2	sin	ω
		ω		ω		2

= lim_{ω → 0}		2.cos ω	+ 2 cos	ω	.	1
		1		2		2

= 2 + 1 = 3.
Hence, alternative (D) is the correct choice.