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Using the radio velocity convention

In this framework, the generalization is straightforward. The frequency axis can then be described with

\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{r...
...mathrm{sys}}}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}},
\end{displaymath} (49)

And the velocity axis with
\begin{displaymath}
\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm...
...{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath} (50)

The velocity axis is given in the observation frame (i.e. $\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{}}}}
\ensuremath{\equiv}\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}$ and $\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{...
...ath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}}$) when $\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} \ne
0$, and in the source/rest frame (i.e. $\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{}}}} \ensuremath{\equiv}\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{sou}}}}$ and $\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{...
...ath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{sou}}}}}$) when $\ensuremath{z_{\ensuremath{\mathrm{}}}}\ne 0$.



Gildas manager 2015-03-19