title: Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform.
abstract: The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.
authors.affiliation: Department of Electrical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan. djj@cc.ee.ntu.edu.tw
authors.forename: Jian-Jiun
authors.initials: JJ
authors.lastname: Ding
authors.forename: Soo-Chang
authors.initials: SC
authors.lastname: Pei
authors.forename: Chun-Lin
authors.initials: CL
authors.lastname: Liu