Nonuniform fast linear canonical transform based on low rank approximation

The investigations of the discrete and fast linear canonical transform (LCT) are becoming one of the hottest research topics in modern signal processing and optics. Among them, the fast calculation of LCT for nonuniform data is one of the key problems. In this paper, two novel fast algorithms based on low-rank approximation are presented. First, we propose two methods for approximate nonuniform time-domain sampling with uniform sampling. Second, we utilize a low rank matrix to approximate the nonuniform LCT kernel, combined with the exponential function and Taylor series. Then, the fast algorithms for nonuniform sampling in the time domain are developed, which cost $K$ FFTs. Finally, we extend the fast algorithm to nonuniform LCT in the frequency and transform domains. The effectiveness of the proposed algorithm is verified by simulations.