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

382.4 Time-Frequency Analysis of Linear FMThis section describes the estimation of the instantaneous frequency using the fourpreviously introduced TF analysis techniques; the Short-Time Fourier transform, theGabor expansion, the Continuous Wavelet transform and the Wigner-Ville distribution.Analytic expressions for the output of each method to a given linear FMsignal are developed and it is shown how the chirp rate can be extracted using eachtechnique. The performance in the presence of additive white Gaussian noise iscompared with the Cramér-Rao bound analytically for the WVD and by simulationsfor all four techniques.2.4.1 The Wigner-Ville Distributionthe WVD is given byusing Equation 2.32 explicitly. For the discrete finite time duration waveform z(n)..a n2T2eJ2 , the WVD is given byThe magnitude squared of the WVD is then given byconverges to the well known limiting form Equation 2.39.Figure 2.19(a) shows the WVD of a linear FM signal with a chirp rate of 0.00117Hz/sec. The window size of the WVD is 64 points. A 3-D mesh plot of this signal isshown in Figure 2.19(b). The chirp may be seen clearly in these figures.