Compressed Sampling of LFM Signals Based on Fractional Fourier Domain

In response to the challenge posed by excessively high sampling rates resulting from the wide bandwidth of linear frequency modulation (LFM) signals, we exploit the inherent sparsity of LFM signals in the fractional Fourier transform (FRFT) domain. By applying a two-step search method to estimate the optimal order, we construct an orthogonal basis dictionary for discrete fractional Fourier transform corresponding to this order. Integrating principles from compressed sensing (CS) theory, we propose a novel LFM signal compressed sampling method based on the FRFT domain. This method compresses and reconstructs LFM echo signals while simultaneously considering the impact of varying digitalizing bit depths during the analog-to-digital converter (ADC) process. Simulation results demonstrate that our approach achieves a favorable sparse representation of LFM signals, enabling signal reconstruction at approximately 10% of the Nyquist rate, while also exhibiting some attenuation of quantization noise and white Gaussian noise.