Sparsity-based time-frequency representation of FM signals with burst missing samples

In this paper, we present an effective time-frequency (TF) analysis of non-stationary frequency modulated (FM) signals in the presence of burst missing data samples. The key concept of the proposed work lies in the reliable sparse recovery of non-parametric FM signals in the joint-variable domains. Specifically, by utilizing the one-dimensional Fourier relationship between the instantaneous auto-correlation function (IAF) and the TF representation (TFR), the proposed approach iteratively recovers missing samples in the IAF domain through sparse reconstruction using, e.g., the orthogonal matching pursuit (OMP) method, while maintaining the TF-domain sparsity. The proposed method, referred to as missing data iterative sparse reconstruction (MI-SR), achieves reliable TFR recovery from the observed data with a high proportion of burst missing samples. This is in contrast to the existing sparse TFR recovery methods which work well only for random missing data samples. In particular, when applied in conjunction with signal-adaptive TF kernels, the proposed method achieves effective suppression of both cross-terms and artifacts due to burst missing samples. The superiority of the proposed technique is verified through analytical results and numerical examples.