Improved Time-Frequency Representation of Multi-Component FM Signals with Compressed Observations

Compressed data measurements of non-stationary signals, which may arise from intentional signal undersampling or missing data samples, introduce undesirable artifacts in the rendered time-frequency (TF) representations. In particular, for multi-component non-linear frequency modulated (FM) signals with distinct amplitudes, such artifacts pose a great challenge to accurately reconstruct weaker signal components. In this paper, we develop improved TF representations that enable accurate instantaneous frequency estimation of such signals, achieve high energy concentration, and provide effective cross-term and artifact mitigation. The proposed technique utilizes a combination of iterative data interpolation in the time-lag domain to recover missing entries and a signal-adaptive TF kernel to suppress cross-terms and artifacts. Simulation results confirm the effectiveness of the proposed method.