Fourier transform rotation invariant

1. Is Fourier transform rotation invariant?
2. Is Fourier transform a rotation?
3. What are rotation invariant features?
4. Are neural networks rotation invariant?

Is Fourier transform rotation invariant?

The continuous-parameter Fourier transform FT is rotationally invariant; that is, if with R a rotation matrix, then .

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 are rotation invariant features?

In mathematics, a function defined on an inner product space is said to have rotational invariance if its value does not change when arbitrary rotations are applied to its argument.

Are neural networks rotation invariant?

Unless your training data includes digits that are rotated across the full 360-degree spectrum, your CNN is not truly rotation invariant.