If X(jω) = 2πδ(ω) + πδ(ω – 4π) + πδ(ω + 4π)

Inverse Fourier transform of X(jω) is given as

x(t) =	1		^∞	X(jω).e^jωtdω
	2π		_{– ∞}

x(t) =	1		^∞	[2πδ(ω) + πδ(ω – 4π) + πδ(ω + 4π)].e^jωtdω
	2π		_{– ∞}

x(t) =	1	[2π + π.e^j4πt + πe^–j4πt]
	2π

= 1 +	1e^j4πt	+	1	e^–j4πt
	2		2

= 1 + cos 4πt