Hartley, cosine and sine fractional transforms over Finite Fields

We introduce finite field versions of fractional Hartley, sine and cosine types 1 and 4 transforms using a matrix function approach. The proposed definitions employ a finite field extension of matrix functions, which does not require the construction of an eigenvector set of the corresponding transform. We also present a relationship between the Fourier and the Hartley fractional matrices and make a preliminary discussion concerning application scenarios for the developed theory.