Simplified chirp dictionary for time-frequency signature sparse reconstruction of radar returns

In sparse reconstruction of the Doppler frequency, the chirp atom approach has been shown to give a better performance than its sinusoidal counterpart. Nevertheless, the chirp atom has a relatively large dimension and so its computational load is much greater compared to the sinusoidal atom. In this paper, we propose a simplified chirp dictionary that obtains a satisfactory time-frequency signature approximation of the signals, but with a computational load comparable to the sinusoidal atom. We estimate the chirp rate through the DTFT of the bilinear product at a certain lag, and the initial frequency is solved in the time domain.