Page 274 - Fundamentals of Radar Signal Processing

FIGURE 4.28 Contour plot of the ambiguity function of an LFM waveform with
βτ = 10.

The zero-Doppler cut of the LFM ambiguity function is the matched filter

output when there is no Doppler mismatch:

(4.99)

This function was illustrated for BT products of both 10 and 100 in Fig. 4.25.
The Rayleigh resolution of the LFM pulse is obtained by examination of Eq.
(4.99). The peak of A(t, 0) occurs at t = 0. The first zero occurs when the
argument of the numerator equals π, which occurs when βt(1–|t|/τ) = 1. For

positive t, this becomes

(4.100)

The roots of this equation are . Since the
argument of the square root in the last expression is less than one, taking the
negative sign gives the positive root closest to zero and thus the Rayleigh

resolution in time. This result can be simplified with the following series