Discrete Fourier transform and automorphism

Abstract. It is well known that in the discrete Fourier transform of a real vector, the components are not completely independent of each other, namely, in the case of \(1\le i <n\), in the transformed vector the component belonging to the index \(n-i\) is the conjugate of the \(i\)-th component. In the following article, we generalize this fact to the case of an arbitrary field and an arbitrary automorphism of that field.

Key words and phrases. Discrete Fourier transform, automorphism.