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

36artifacts called cross-components. The cross-Wigner distribution of two signals, s 1and 32 isThe Wigner-Ville distribution of a two-component signal,The Wigner distribution of the sum of two signals is not the sum of the Wignerdistributions of each signal. For Ws,, thefirst two terms are the auto-componentsof the Wigner distribution of s 1 and s2 . The last term is the cross-component and ismade up of two overlapping components, W and W s2,. The cross-component islocated midway between the two auto-components on the time-frequency plane andoscillates with a spatial frequency that is inversely proportional to their separation[23].In a multicomponent signal, one cross-component will appear between eachpair of auto-components. The number of cross-components increases quadraticallyas the number of components in the signal increases. A n-component signal hascross-components. These make the WVD of multicomponent signals difficult tointerpret and enhance noise.In Figure 2.18, the WVD of the signal of Equation 2.10 is shown with the threecross-components.2.3.4.2 Discrete form of the Wigner Distribution: The discrete Wignerdistribution (DWD) with a discrete frequency variable is defined for a discrete timesignal by• I