Space/time/frequency methods in adaptive radar - New Jersey ...

34representations are bilinear (quadratic) in the signal transformation. The Wigner-Ville distribution (WVD) was the first proposed bilinear Time-Frequency Distribution(TFD) [2]. The WVD of a signal s(t) is given by:The WVD of s(t) = sin(2πƒt) is shown in Figure 2.17. As shown in thisexample, the frequency response of the sample signal is not smooth.It may be shown that the various transforms are related to one another. TheSTFT can be expressed in terms of the WVD with the expression [23]where Wg is the WVD of the STFT analysis window. The Gabor expansion and theWVD are related through the physical spectrum [40] given byThe scalogram may be written using Cohen's class for bilinear time-frequencyenergy distributions [41, 42] aswhere W, is the WVD of the analyzed signal, z(t) and Wh is the WVD of the basicas time and frequency.2.3.4.1 Cross-components: The WVD possesses a number of important mathematicalproperties that are detailed in [2, 43]. The WVD has limitations when usingit as a practical time-frequency analysis technique due to the presence of nonlinear