New Smoothed Time-Frequency Rate Representations for Suppressing Cross Terms

In this paper, to suppress the cross terms in a time-frequency rate representation (TFRR), we propose four kinds of smoothed TFRRs (STFRRs) based on high resolution TFRR (HR-TFRR) and cubic phase function. We first define two types of ambiguity functions of TFRR (AF-TFRR) and give a relationship between AF-TFRRs and TFRRs. Then, a mask is devised to extract the auto terms and suppress the cross terms in AF-TFRR domain. Finally, four STFRRs are obtained based on the masked AF-TFRRs. STFRRs are suitable for a signal composed of multiple linear frequency modulated components or cubic phase components with small third order parameters. To analyze a signal composed of multiple cubic phase components with large third order parameters, we propose smoothed time-chirp rate representations (STCRRs) in the same way as STFRRs. Numerical examples demonstrate that STFRRs and STCRRs can suppress the cross terms effectively.