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The Ambiguity function (AF) is the operators that are related to the WDF.<br>
:<math>A_{x}(\tau,n) = \int^\infty_{-\infty}x(t+\frac{\tau}{2}) x^{*}(t-\frac{\tau}{2}) e^{-j 2 \pi tn} dt</math><br>
(1)If <math>x(t) = exp[-\alpha\pi{(t-t_{0})^2} + j2\pi f_{0}t]</math><br>
:<math>A_{x}(\tau,n)</math>
:<math>= \int^\infty_{-\infty}e^{-\alpha\pi (t+\tau/2-t_{0})^{2}+j2\pi f_{0}(t+\tau/2)}+e^{-\alpha\pi (t-\tau/2-t_{0})^{2}-j2\pi f_{0}(t-\tau/2)}e^{-j2\pi tn}dt</math>
:<math>= \int^\infty_{-\infty}e^{-\alpha\pi [2(t-t_{0})^{2}+\tau^{2}/2]+j2\pi f_{0}\tau}e^{-j2\pi tn}dt</math>
:<math>= \int^\infty_{-\infty}e^{-\alpha\pi [2t^{2}-\tau^{2}/2]+j2\pi f_{0}\tau}e^{-j2\pi tn}e^{-j2\pi t_{0}n}dt</math>
:<math>A_{x}(\tau,n) = \sqrt\frac{1}{2\alpha}exp[-\pi (\frac{\alpha\tau^{2}}{2}+\frac{n^{2}}{2\alpha})]exp[j2\pi (f_{0}\tau-t_{0}n)]</math>
<br>
[[File:Wdf Ambiguity function plane.png|thumb|Wdf Ambiguity function plane]]
WDF and AF for the signal with only 1 term<br>
(2) If <math>x(t) = exp[-\alpha_{1}\pi (t-t_{1})^{2}+j2\pi f_{1}t] + exp[-\alpha_{2}\pi (t-t_{2})^{2}+j2\pi f_{2}t]</math>
== See also ==
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