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

Abstract

Missing samples and randomly sampled non-stationary signals give rise to artifacts that spread over both the time-frequency and the ambiguity domains. These two domains are related by a two-dimensional Fourier transform. As these artifacts resemble noise, the traditional reduced interference signal-independent kernels, which belong to Cohen’s class, cannot mitigate them efficiently. In this paper, a novel signal-independent kernel in the ambiguity domain is proposed. The proposed method is based on three important facts. Firstly, any windowed non-stationary signal can be approximated as a sum of chirps. Secondly, in the ambiguity domain, any chirp resides inside certain regions, which just occupy half of the ambiguity plane. Thirdly, the missing data artifacts always appear along the Doppler axis where the chirps auto-terms do not appear. Therefore, we propose using a chirp-based fixed kernel on windowed non-stationary signals in order to remove half of the noise-like artifacts in the ambiguity domain and compensate for the missing data effect located along the Doppler axis. It is shown that our method outperforms other reduced interference time-frequency distributions.