The fractional Fourier transform over finite fields

The central contribution of this paper is the definition of the fractional Fourier transform over finite fields (GFrFT). In order to introduce the GFrFT, concepts related to trigonometry in finite fields are reviewed and some new ideas put forward. In particular, graphic representations of elements in a finite field are suggested and analogies with real and complex numbers are discussed. A modified version of the finite field Fourier transform is given and its eigenstructure is analyzed. This allows us to develop GFrFT theory and investigate its main characteristics. Some illustrative examples are also given throughout the paper.

► A fractional Fourier transform over finite fields is proposed.
► Concepts related to trigonometry in finite fields are reviewed and some new ideas put forward.
► The eigenvector set used in the fractionalization is obtained from a matrix which commutes with the finite field Fourier transform matrix.
► Illustrative examples are given throughout the paper.