This project proposes to construct an observation matrix based on the principle of compressive sensing

using fractional Fourier transform and equivalent time sampling to perform a sparse representation of the observation process

to establish a high frequency observation equation in accordance with the principle of compressive sensing

and to solve it

and finally to realise the reconstruction of the original signal.High-precision reconstruction of linear FM signals can be achieved using time-specific sampling at shorter rates than Nyquist sampling.When sampling is done at unequal intervals

the time-frequency range sampled is no longer fixed in the time-frequency range

but results in a large amount of extraneous perturbation due to energy leakage from non-zero points in the original signal.Equivalent time sampling makes the spectrum no longer move regularly

but a small part of it moves haphazardly

and the frequency leakage is uniformly distributed throughout the frequency domain

thus the leakage values are all smaller

making the recovery process less error-prone.The simulation experiment results show that the proposed method achieves a reconstructed power of 99.62% at 17 sampling points.