On the Multiangle Discrete Fractional Fourier Transform

Abstract: The efficiently computed multiangle centered discrete fractional Fourier transform (MA-CDFRFT) [1] has proven as a useful tool for time-frequency analysis; however, its scope is limited to the centered discrete fractional Fourier transform (CDFRFT). Meanwhile, extensive research on the standard DFRFT has lead to a better understanding of this transform as well as numerous possible choices for eigenvectors for implementation. In this letter we present a simple adaptation of the MA-CDFRFT which allows us to efficiently compute its standard counterpart, which we call the multiangle DFRFT (MA-DFRFT). Furthermore, we formalize the symmetries inherent to the MA-CDFRFT and MA-DFRFT to halve the number of FFTs needed to compute these transforms, paving the way for applications in resource constrained environments.