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Ambiguity Function
Levanon & Mozeson — Waveform Analysis for Radar
Waveform
Rectangular Pulse
LFM Chirp
Barker-13
V-shaped LFM (up+down)
Parameters
Pulse Width T (μs)
10
Bandwidth B (MHz)
5
Cut Axis
Delay τ cut (at f
d
)
0
Hz
Doppler f
d
cut (at τ)
0
μs
Ambiguity Function
|χ(τ, f
d
)|² = |∫ s(t)s*(t-τ)e
j2πf
d
t
dt|²
Thumbtack:
Ideal — narrow in both τ and f
d
Rect pulse:
Good delay res, poor Doppler res (sinc in f
d
)
LFM:
Coupled τ-f
d
(ridge tilted by B/T slope)
Volume invariance:
Total volume is constant — narrowing one axis spreads the other.