Some properties of the generalized time frequency representation with cone-shaped kernel

The cone-shaped kernel generalized time-frequency representation (GTFR) of Zhao, Atlas, and Marks (ZAM) has been shown empirically to generate quite good time frequency representation in comparison to other approaches. The authors analyze some specific properties of this GTFR and compare them to other TFRs. Asymptotically, the GTFR is shown to produce results identical to that of the spectrogram for stationary signals. Interference terms normally present in many GTFRs are shown to be attenuated drastically by the use of the ZAM-GTFR. The ability of the ZAM-GTFR to track frequency hopping is shown to be close to that of the Wigner distribution. When a signal is subjected to white noise, the ZAM-GTFR produces an unbiased estimate of the ZAM-GTFR of the signal without noise. In many other GTFRs, the power spectral density of the noise is superimposed on the GTFR of the signal. It is also shown that, in discrete form, the ZAM-GTFR is generally invertible