An Analysis of 2-D Signals With Fast Varying Instantaneous Frequencies: Extending Complex-Lag Time-Frequency Distribution

The radar echo of a target can be modeled as a 2-D signal whose variables are the intra-pulse sampling time (fast-time) and the inter-pulse sampling time (slow-time).The fast-time instantaneous frequency (FIF) and slow-time instantaneous frequency (SIF) of the signal are modulated by the target's slant range. When the target undergoes complex motion, the radar echo becomes a 2-D signal with fast-varying instantaneous frequencies (IFs). IF analysis for such a signal is challenging. To solve this issue, an extending complex-lag time-frequency distribution (ECTD) is introduced. ECTD is a 3-D distribution for 2-D signals based on traditional complex-lag time-frequency distribution (CTD), and it inherits the good performance in handling fast-varying IFs.By introducing complex-lags in both the fast-time and slow-time dimensions, the ECTD can accurately estimate the SIF and FIF of a 2-D signal with fast-varying IFs. Finally, a reduced interference realization of the ECTD achieved by introducing the frequency domain filter is given. Numerical examples validate the effectiveness of the ECTD.