Two‐dimensional sparse fractional Fourier transform and its applications

The discrete fractional Fourier transform is an excellent tool in non-stationary signal processing. And an efficient and accurate computation is important for the two-dimensional discrete fractional Fourier transform (2D DFRFT). Inspired by the sparse Fourier transform algorithm, we propose a two-dimensional sparse fractional Fourier transform (2D SFRFT) algorithm to estimate the fractional Fourier spectrum efficiently. Compared with existing methods, we have achieved the lowest runtime and sample complexity. Moreover, by analyzing the errors due to noises, the 2D SFRFT algorithm is improved to be robust. The applications in image fusion, parameter estimation of multicomponent 2D chirp signal and complex maneuvering targets in SAR radar demonstrate the effectiveness of the proposed algorithms.