
Fast Fourier Transform
Hi all. I am not positive if this is the correct forum for this thread, but it has to do with numerical analysis so I assume it will do.
Anyway, I am having trouble finding the correct way to do this problem, and have been working on it for hours. I feel I can almost get the answer, but just not quite. If you all could take a look and help me out, that would be awesome.
The Discrete Fourier transform is as follows:
exp
for
There is more information given to me from previous parts in the problem that help answer the question at hand, so here it is:
1) Not sure how relevant this is, but:
for and is the complex conjugate of (as in all complex variables change signs)
2) If and are the corresponding DFTs, then:
Here comes the issue at hand:
Express in terms of
I'm confused because it seems like is simply the rewrite of divided into even and odd terms (FFT), but there's the i in front of , so I'm not sure what to do with that.
Then I tried manipulating the two equations: and to plug into the even and odd breakdown of , but got something weird. Any insight is more than welcomed. Thank you