A multi-input-multi-output system approach for the computation of discrete fractional Fourier transform

Abstract In the last decade, there have been several approaches on the topic of computing discrete fractional Fourier transform (DFrFT). The purpose of this work is to provide a unified approach to improve the computation of DFrFT. Based on results by Ozaktas et al., a more general multirate filter structure is developed for the improvement of computing DFrFT. With introduction of block-input–block-output technique, a specific multirate filtering system can be converted to an equivalent linear time-invariant (LTI) multi-input–multi-output (MIMO) system. Other DFrFT algorithms based on matrix–vector multiplication can also be implemented by the similar structure. Therefore, a unified computation framework is developed for the multirate implementation of the DFrFT via the proposed MIMO system. Finally, for the implementation of DFrFT system, a corresponding fractional Fourier filter bank (FrFB) is also constructed as an extension of the conventional discrete Fourier transform (DFT) filter bank system.