A moving target causes addition frequency shifting of the echo signal due to the Doppler effect, which can be expressed by the following relationship:
<math> f_{Rx} = f_{Tx} \left( \frac{1+v/{c}}{1-v/c} \right) </math>
where f<sub>Tx</sub> and f<sub>Rx</sub> are the frequency of the transmitted and received signals respectively, and v<sub>r</sub> is the relative velocity of the target with respect to the radar system. The frequency shift due to the target's velocity is then given by:
<math> f_d = f_{TxRx} - f_{RxTx} = 2 f_{Tx}\frac{v_r}{c-v_r} \approx \frac{2v_r}{\lambda_0} </math>
where and λ<sub>0</sub> = c/f is the free=space wavelength, and it was assumed that v<sub>r</sub> << c.
== Exploring FM Modulation ==