Title The Discrete Factional Fourier Transform on the GDFT Matrix Type Presentation Keywords Discrete Tigonometric Tansform, Discrete Fractional Fourier Transform, Eigenvalues, Eigenvectors Abstract A novel discrete fractional Fourier transform (DFrFT) based solely on the GDFT matrix is introduced for a special case. Eigenvectors of the G matrix are derived in a straightforward manner, and the multiplicity of eigenvalues has also been computed. Researchers Ali Bagheri-Bardi (Second researcher) , Taher Yazdanpanah (Third researcher)