Discrete fractional Fourier transform based on the eigenvectors of Grünbaum tridiagonal matrix

The development of the discrete fractional Fourier transform (DFRFT) necessitates the availability of a complete set of orthonormal eigenvectors of the DFT matrix F. An eigenanalysis is performed for the original Grünbaum tridiagonal matrix T - which commutes with matrix F - having only one eigenvalue of multiplicity two and simple remaining eigenvalues. The two easily obtainable eigenvectors of T corresponding to its repeated eigenvalue - which are not eigenvectors of F - are exploited for analytically generating two orthonormal eigenvectors common to both T and F.