Compressive sensing based separation of LFM signals

A compressive sensing approach for separation of linear frequency modulated signals from non-stationary disturbance is proposed. The linear time-frequency representation is achieved using the Local Polynomial Fourier Transform (LPFT), which allows revealing data local behavior. Based on the LPFT, the frequency-chirp rate domain is used to achieve sparse signal representation. Then the LPFT is combined with the L-statistics to collect only the time-frequency points belonging to the desired signal, while the points belonging to overlapping regions and disturbance are deemed inappropriate and omitted from observations. The relationship between the measurement and sparsity domain is established in order to use the compressive sensing concept and to completely recover the desired signal. The theory is proven on examples.