Nonuniform fast linear canonical transform

The linear canonical transform (LCT) is a generalized form of the Fourier transformation. It has been shown to be one of the most powerful tools in applied mathematics, signal processing and optics fields. The aim of this paper is to present a nonuniform fast linear canonical transform (NFLCT), which emerges in many areas of physics and engineering. The proposed algorithm generalizes the fast linear canonical transform to the case of non-integer frequencies on the interval [-bπ, bπ]. The algorithm requires O(N logN + N log(1/ϵ)) arithmetic operations where ϵ is the precision of computations and N is the number of nodes. The efficiency of the approach is illustrated by simulations.