Fractional cosine and sine transforms over finite fields

In this paper, we introduce fractional cosine and sine transforms over finite fields. The basis for the definition of such transforms, which are respectively referred by the acronyms GFrCT and GFrST, is the recently proposed fractional Fourier transform over finite fields (GFrFT) [1]. More specifically, we use the eigenvectors of the finite field Fourier transform to construct eigenvectors of the finite field cosine and sine transforms. Such eigenvectors are then used in spectral expansions that allow to compute fractional powers of the finite field cosine and sine transform matrices.