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jkface
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Homework Statement
Find the inverse Fourier transform of F(jω) = cos(4ω + pi/3)
Homework Equations
δ(t) <--> 1
δ(t - to) <--> exp(-j*ωo*t)
cos(x) = 1/2 (exp(jx) + exp(-jx))
The Attempt at a Solution
So first I turned the given equation into its complex form using Euler's Formula.
F(jω) = 1/2 (exp(j*4*ω + j*pi/3) + exp(-j*4*ω - j*pi/3))
And using the relevant equation above, I get..
exp(j*4*ω) <--> δ(t + 4) and exp(j*4*ω) <--> δ(t - 4)
I'm not exactly sure how to do inverse Fourier transformation on exp(j*pi/3) and exp(-j*pi/3). My guess is you simply get simply exp(j*pi/3)*δ(t) and exp(-j*pi/3)*δ(t).
Assuming I'm correct in the above step, I now multiply the resulting expressions.
1/2 ( exp(j*pi/3)*δ(t)*δ(t + 4) + exp(-j*pi/3)*δ(t)*δ(t - 4) )
Is my solution correct? I feel like I would have to simply the final answer I got but I'm not really sure how.
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