Abstract
Abstract The fractional Fourier transform (FRFT) is a powerful tool for time-varying signal analysis. There exist various discrete fractional Fourier transforms (DFRFTs); in this paper, we systematically analyze and compare the main DFRFT types: sampling-type DFRFTs and eigenvector decomposition-type DFRFTs. First, for the existing sampling-type DFRFTs, we perform concrete analyses and comparisons of their applicable conditions and then establish their equivalence relationship. Then, for various eigenvector decomposition-type DFRFTs, their common mechanisms are extracted and thus they are effectively classified. In addition, as the extended version of DFRFTs, discrete counterparts of the linear canonical transform (LCT) and simplified FRFT (SFRFT) are summarized and classified. Our work is instructive for research about the choice of a more appropriate DFRFT in different applications, which is also supported by simulation experiments. Finally, for the DFRFT, DLCT and DSFRFT, two applications regarding detection for chirp signals and optical imaging are investigated to intuitively analyze their differences.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
