Page 245 - Fundamentals of Radar Signal Processing

FIGURE 4.9 Contour plot of the simple pulse ambiguity function of Fig. 4.8.

The zero-Doppler response A(t, 0) gives the matched filter output when
there is no Doppler mismatch. Setting F = 0 in Eq. (4.51) and using
D
L’Hôpital’s rule to resolve the indeterminate form gives

(4.52)

Similarly, the zero-delay cut A(0, F ) gives the output of the matched filter at the
D
expected peak time t = 0 as a function of Doppler mismatch. Using t = 0 in Eq.
(4.51) immediately gives

(4.53)

Equations (4.52) and (4.53) are the expected triangle and sinc functions derived
previously. They are illustrated in Fig. 4.10.