TY - JOUR
T1 - Analysis and comparison of discrete fractional fourier transforms
AU - Su, Xinhua
AU - Tao, Ran
AU - Kang, Xuejing
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/7
Y1 - 2019/7
N2 - 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.
AB - 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.
KW - Commuting matrices
KW - Eigenvector decomposition
KW - Fractional fourier transform
KW - Linear canonical transform
UR - https://www.scopus.com/pages/publications/85062593753
U2 - 10.1016/j.sigpro.2019.01.019
DO - 10.1016/j.sigpro.2019.01.019
M3 - Review article
AN - SCOPUS:85062593753
SN - 0165-1684
VL - 160
SP - 284
EP - 298
JO - Signal Processing
JF - Signal Processing
ER -