where and λ<sub>0</sub> = c/f is the free=space wavelength, and it was assumed that v<sub>r</sub> << c.
Â
<math> f_{bu} = f_b - f_d \\
f_{bd} = f_b + f_d </math>
Â
where f<sub>bu</sub> and f<sub>bd</sub> are the beat frequencies during the up-ramp and down-ramp sweeps, respectively. The target range and velocity are then calculated from the following equations:
Â
<math> R = \frac{cT_s}{4B} \left( f_{bd} + f_{bu} \right) </math>
Â
<math> v_r = \frac{\lambda_0}{4} \left( f_{bd} - f_{bu} \right) </math>
== Exploring FM Modulation ==