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Principle

Changing the source systemic velocity is a change of source reference frame. The signal and image frequency scales in the measurement frame must stay constant under this transform. However they change in the source reference frame. Indeed

\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{m...
...ath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{rest}}}},
\end{displaymath} (89)

with
\begin{displaymath}
\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mat...
...hrm{sys,new}}}^{\ensuremath{\mathrm{meas}}}}}{\ensuremath{c}}.
\end{displaymath} (90)

Hence
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathr...
...{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}}.
\end{displaymath} (91)



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