Sparse discrete linear canonical transform and its applications

•A new sampling framework in the sparse linear canonical domain is proposed to work with large data sets more effectively.•Ensuring sparsity of the frequency domain and removing redundant data of the signal by exploiting the sparse Fourier transform.•The sparse discrete linear canonical transform is proposed.•The sparse linear canonical-matched filtering process of LFM signal is derived and applied to pulse compression of the LFM signal.•The paper applies the proposed algorithm to moving target detection for synthetic aperture radar and obtains good detection performance. The linear canonical transform (LCT) is a powerful tool for non-stationary signals in signal processing. In this paper, we propose a sparse discrete linear canonical transform (SDLCT) algorithm to solve the high sampling rate and large data calculation of non-stationary signals. In detail, we introduce permutation of spectra and window function to ensure the sparsity of the frequency domain. To get rid of the redundant data of the signal and improve the processing efficiency, we compress the high-dimensional signal into the low-dimensional signal by down-sampling. Then the low dimensional signal is mapped to a linear canonical domain. The above processes effectively reduce the amount of data and computation for signal processing. Then, we apply the SDLCT to the pulse compression of the linear frequency modulation (LFM) signal. The comparison between SDLCT and LCT shows that SDLCT is hardly affected by noise, it can accurately obtain the target positions at a low signal-to-noise ratio (SNR). Furthermore, we apply this algorithm to moving target detection for synthetic aperture radar. The comparison between LCT, sparse Fourier transform (SFT), sparse discrete fraction Fourier transform (SDFrFT), and SDLCT shows that SDLCT has stronger signal detection performance and can detect all the signals that affect each other.