I have an image and its fourier transform. When I rotate it, its fourier transform rotates too, but I can't figure it out. Why does this happen? On the other hand, when I shift the image, its fourier transform doesn't change. As I know, time shifting means frequency shifting. Am Iwrong?

enter image description here


1 Answer 1


Time shift corresponds to a phase shift in frequency domain, not a frequency shift. Since you display only the magnitude of the 2D FFT before and after the shift, you do not observe the phase shift.

$$f(x) \Rightarrow F(w) \\ f(x-a) \Rightarrow e^{-j2\pi wa} F(w) $$

Rotation in space corresponds to a rotation in frequency domain as you observe.

For proofs, see these notes on Some Properties of Fourier Transform


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.