Abstract:  In order to solve the problem of acquisition, storage and transmission for linear frequency modulated (LFM) signals, a novel analog-to-information conversion method based on α-random demodulator is proposed. With the proposed system, both the sampling frequency and sample number can be reduced significantly during the compressive sampling. Utilizing the sparsity of LFM signals in fractional Fourier domain, the compressive sampling process was achieved by the proposed α-random demodulator. Then, we analyzed the working process for α-random demodulator systematically. The relationship between system output and sparse vector of LFM signals was presented. And based on this relationship, we further established the mathematical reconstruction model for α-random demodulator to reconstruct the sparse vector of LFM signals. Finally, the reconstruction was achieved by solving the convex optimization problem. And the accurate reconstruction for original signals is obtained. The effectiveness of the proposed scheme was verified by numerical experiments. We show that the proposed analog-to-information conversion method achieves the effective compressive sampling and accurate reconstruction for LFM signals. Compared with the other analog-to-information conversion methods, we reduced the complexity of dictionary construction during the reconstruction process.