Complementary Pair Radar Waveforms Figure 7. The frequency response of the 2-pulse canceller (top), the weighted FFT (middle), and the combined response (bottom), for the fourth Doppler window. subplot. It is the combined Doppler response at zero delay. The responses in Figure 7 are Doppler frequency responses. To see the delay-Doppler response we need to add the 2-pulse canceller and recalculate Figure 4. The resulting delay-Doppler response is shown in Figure 8. The calculation used the actual complementary pulse pairs, making the periodicity 2Tr instead of Tr. That explains the additional Doppler ridge at νNTr = N / 2 + 4 = 32 + 4 = 36. Note that the bottom subplot of Figure 7 is the τ / tb = 0 cut of Figure 8, using a log scale of the Doppler axis. Thus, Figure 8 contains much more information than Figure 7. The calculation that yielded Figures 7 and 8 was repeated for Doppler filter νNTr = 1. The results appear in Figures 9 and 10. Note the considerably stronger attenuation by the canceller at that low Doppler shift. 44 Figure 8. Delay-Doppler response. Doppler shift νNTr = 4, 2-pulse canceller, N=64. Zoom on |τ| ≤ tp. IEEE A&E SYSTEMS MAGAZINE MARCH 2017