Fully fledged versus simple fractional discrete Fourier transform of type IV

The fractional discrete Fourier transform of type IV (FDFT-IV) is a generalization of the discrete Fourier transform of type IV (DFT-IV). The paper presents a fully-fledged definition for the FDFT-IV which necessitates the availability of orthonormal eigenvectors of the DFT-IV matrix G. This definition is shown to outperform the simple definition which is just a linear combination of the signal, its DFT-IV and their flipped versions.