TY - JOUR
T1 - Sliding 2D Discrete Fractional Fourier Transform
AU - Liu, Yu
AU - Miao, Hongxia
AU - Zhang, Feng
AU - Tao, Ran
N1 - Publisher Copyright:
© 1994-2012 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - The two-dimensional discrete fractional Fourier transform (2D DFrFT) has been shown to be a powerful tool for 2D signal processing. However, the existing discrete algorithms aren't the optimal for real-time applications, where the input signals are stream data arriving in a sequential manner. In this letter, a new sliding algorithm is proposed to solve this problem, termed as the 2D sliding DFrFT (2D SDFrFT). The proposed 2D SDFrFT algorithm directly computes the 2D DFrFT in current window using the results of previous window, which greatly reduces the computations. During the derivation, we find that the (m+δn)th DFrFT bin in previous window is needed for computing the (m,n)th DFrFT bin in current window, where the increment δ isn't always an integer. Further, a method is proposed to convert the increment δ to a certain integer by determining appropriate sampling interval. The theoretical analysis demonstrates that when compute the new 2D DFrFT in a shifted window in sliding process, our proposed algorithm has the lowest computational cost among existing 2D DFrFT algorithms.
AB - The two-dimensional discrete fractional Fourier transform (2D DFrFT) has been shown to be a powerful tool for 2D signal processing. However, the existing discrete algorithms aren't the optimal for real-time applications, where the input signals are stream data arriving in a sequential manner. In this letter, a new sliding algorithm is proposed to solve this problem, termed as the 2D sliding DFrFT (2D SDFrFT). The proposed 2D SDFrFT algorithm directly computes the 2D DFrFT in current window using the results of previous window, which greatly reduces the computations. During the derivation, we find that the (m+δn)th DFrFT bin in previous window is needed for computing the (m,n)th DFrFT bin in current window, where the increment δ isn't always an integer. Further, a method is proposed to convert the increment δ to a certain integer by determining appropriate sampling interval. The theoretical analysis demonstrates that when compute the new 2D DFrFT in a shifted window in sliding process, our proposed algorithm has the lowest computational cost among existing 2D DFrFT algorithms.
KW - 2D algorithm
KW - fractional fourier transform
KW - sliding window
KW - two-dimensional discrete fractional Fourier transform
UR - http://www.scopus.com/inward/record.url?scp=85077760554&partnerID=8YFLogxK
U2 - 10.1109/LSP.2019.2945128
DO - 10.1109/LSP.2019.2945128
M3 - Article
AN - SCOPUS:85077760554
SN - 1070-9908
VL - 26
SP - 1733
EP - 1737
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
IS - 12
M1 - 8854972
ER -