The cross Time-Frequency Distribution Series for Synthetic Aperture Radar (SAR) applications

Joint Time Frequency Analysis (JTFA) is a powerful analysis tool in SAR image processing. At the heart of this process are the Time-Frequency Representations (TFR´s) such as the Wigner-Ville distribution (WVD), which is difficult to use because of its large cross-product terms. The pseudo-WV TFR reduces the cross terms by smoothing the integration defining the WV transform. The Time-Frequency Distribution Series (TFDS) mitigates the unwanted cross product terms by averaging only those expansion terms close to the signal. The cross-Wigner-Ville Distribution (CWVD) is a generalization of the cross correlation function to the time-frequency (TF) plane. Likewise, the cross- pseudo-WV and the cross-TFDS can be defined and applied to pairs of signals. The cross-TFDS is shown to reduce the cross terms seen in the cross-WV distribution. Two examples are shown using SAR data.