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FIGURE 4.7 “Thumbtack” ambiguity function.
4.4.2 Ambiguity Function of the Simple Pulse
As a first example of an ambiguity function, consider a simple pulse centered on
the origin and normalized to have unit energy (E = 1) for convenience
(4.48)
Applying Eq. (4.30) gives for t > 0
(4.49)
The ambiguity function for t > 0 is the magnitude of Eq. (4.49)
(4.50)
Repeating the derivation for t < 0 gives a similar result, but with the quantity (τ
– t) replaced by (τ + t). The complete AF of the simple pulse is therefore
