# 1-D Fourier Transform Of A 2-D Image But At An Arbitrary Orientation

If one has a 2-D array and would like to take the 1-D Fourier transform along a direction $\theta$ degrees off the horizontal, is there a better/faster way to do this rather than rotating the image by $-\theta$ degrees, taking the 1-D FT across the columns, and then rotating the result back by $\theta$ degrees?

• Well 2DFFT(rotated(image)) = rotated(2DFFT(image)), right? So I doubt there's any shortcut for 1DFFT. – endolith Oct 8 '13 at 0:27

Possible choices for the angle $\theta$ are going to be limited. but the transform will be free from interpolation artifacts introduced by the rotation algorithm.
• I'm not worried about artifacts since I can use high quality filters in the resampling. It's more about efficiency. Also, $\theta$ really needs to be given to several decimal places, so a psuedo-polar FFT is not a solution. – AnonSubmitter85 Oct 4 '13 at 21:50