Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

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 :(

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Inverse Fourier Transform

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**