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

42It is very clear from Equations 2.39 and 2.44 that the spectrum of z(t) isconcentrated along the line 2πƒ = pit and equivalently mF=µnT. The concentrationrepresents the instantaneous frequency. The sampled spectrum given byEquation 2.44 can also be computed from the weighted WVD using Equation 2.33:The Gabor expansion of a linear FM signal with a chirp rate of 0.00117 Hz/secis shown in Figure 2.21(a). The time-frequency plane is represented by a rectangulargrid of size 32x16 with the signal oversampled by a factor of 4. The 3-D mesh plot ofthis signal is shown in Figure 2.21(b). The chirp is clearly displayed in these figuresby the Gabor expansion. The artifact to the right of the time scale is a result of theparameters used in the transform.2.4.4 The Continuous Wavelet TransformUsing Equations 2.34 and 2.39, the scalogram of the linear FM waveformis shown to beAs in the case of the other TF techniques, the instantaneous frequency of the linearFM waveform is represented in this equation.The scalogram of a linear FM signal with a chirp rate of 0.00117 Hz/sec isshown in Figure 2.22(a). The scalogram was analyzed with a window of 32 points at.the coarsest scale. The 3-D mesh plot of this signal is shown in Figure 2.22(4 Asin the other cases, the chirp may be seen in these figures.