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.
Key words
fractional Fourier transform /
equivalent time sampling /
compressive sensing /
chirp signal
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