Is there an analogue to the 2D DFT that is rotation equivariant?

1. Is Fourier transform a rotation?
2. What is 2D DFT in digital image processing?
3. Why is DFT mirrored?
4. Is DFT shift invariant?

Is Fourier transform a rotation?

The Fourier transform is a rotation by 1 2 generated by the oscillator Hamiltonian. It transforms the position operator into the momentum operator p ˆ i in the quantum mechanical case (plane, top); both operators have spectrum R, and each generates (noncommuting) translations of phase space in L 2 (R).

What is 2D DFT in digital image processing?

• As in the 1D case, 2D-DFT, though a self-consistent transform, can be considered as a mean of calculating the transform of a 2D sampled signal defined over a discrete grid. • The signal is periodized along both dimensions and the 2D-DFT can. be regarded as a sampled version of the 2D DTFT.

Why is DFT mirrored?

Because both the positive and negative frequency sinusoids are 90 degrees out of phase and have the same magnitude, they will both respond to real signals in the same way.

Is DFT shift invariant?

In spite of being linear, the Fourier transform is not shift invariant. In other words, a shift in the time domain does not correspond to a shift in the frequency domain.