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

Abstract

Abstract-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.

Time-Frequency Distribution for Undersampled Non-stationary Signals using Chirp-based Kernel

“…According to [8], [9] and [17], the frequency law of any nonstationary windowed signal can be approximated as a sum of chirps. In another words, we can consider any windowed nonstationary signal as built from chirps and so we can apply the chirp-based kernel on the windowed non-stationary segments.…”

“…Thus, we can remove half of the ambiguity domain if the input signals are chirps. Additionally, according to [8] and [9], any non-stationary windowed signal can be approximated as a sum of chirps. So, for any nonstationary signal segment, we can cut half of the ambiguity plane.…”