# Inverse Fourier Transform

1. May 16, 2012

### helderdias

Hi everyone,

I'm trying to solve an exercise in which I need to find x(t) considering that X(ω) = cos(4ω). So, I need to find the Inverse Fourier Transform of cos(4ω), but I don't have the inverse fourier transform table.

So, I thought about applying the duality property. If x(t) <--> X(ω), then X(t) <--> 2π*x(-ω)

cos(4ω) <--> π[δ(ω-4) + δ(ω+4)]

Applying the duality property

π[δ(t-4) + δ(t+4)] <--> 2π.cos(-4ω)

Since cos(x) = cos(-x)

1/2*[δ(t-4) + δ(t+4)] <-->cos(4ω)

Therefore

x(t) = 1/2*[δ(t-4) + δ(t+4)]

Is that correct? WolframAlpha is giving me a different answer :(