On the multiangle centered discrete fractional Fourier transform

Existing versions of the discrete fractional Fourier transform (DFRFT) are based on the discrete Fourier transform (I)FT). These approaches need a full basis of DFT eigenvectors; that serve as discrete versions of Hermite-Gauss functions. In this letter, we define a DFRFT based on a centered version of the DFT (CDFRFT),using eigenvectors derived from the Grunbaum tridiagonal commutor that serve as excellent discrete approximations to the Hermite-Gauss functions. We develop a fast and efficient way to compute the multiangle version of the CDFRFT for a discrete set of angles using the FFT algorithm. We then show that the associated chirp-frequency representation is a useful analysis tool for multicomponent chirp, signals.