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Mathematics
General Math
Informational content in 2D discrete Fourier transform
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[QUOTE="timelessmidgen, post: 6053529, member: 616801"] When you do a discrete Fourier transform (DFT) of a one-dimensional signal, I understand that the second half of the result is the complex conjugate of the first half. If you threw out the second half of the result, you're not actually losing any data and you would be able to recreate the entire signal from just the first half after calculating its complex conjugate and stitching it together (right?) I get confused when it comes to the two dimensional DFT. For the purposes of this conversation I'm assuming the result of the DFT is unshifted (IE all four corners in the two dimensional result correspond to low frequency signals, as opposed to the center as it would be in a shifted result.) When I think about the results I thought all the actual information would be contained within the lower left quadrant, and indeed I know that the numbers in the upper right quadrant will simply be complex conjugates of the numbers in the lower left quadrant. I also know that numbers in the upper left quadrant will be complex conjugates of the numbers in the lower right quadrant, but what is their relation to the numbers in the lower left quadrant (the 'important' quadrant in my mind). Can you recreate the upper left and lower right quadrants if all you have is the lower left quadrant? Or do they actually contain more information? [/QUOTE]
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General Math
Informational content in 2D discrete Fourier transform
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