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Signal and image frequency axes in the rest frame

The discussion of Section [*] is still valid for both the signal and image frequency axes. Eq. [*] can easily be rewritten

\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{sig}}^{\ensuremath{\mathr...
...emath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath} (20)

and
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{ima}}^{\ensuremath{\mathr...
...emath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath} (21)

with
\begin{displaymath}
\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\e...
...athrm{sys}}}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}.
\end{displaymath} (22)

\ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}} is simply the tuning frequency entered by the user. However, \ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{rest}}}} must be computed. The easiest way is to define the side band separation as
\begin{displaymath}
\ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\ma...
...th{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{obs}}}} \right] }.
\end{displaymath} (23)

It is straightfoward to show that it is constant and equal to
\begin{displaymath}
\ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\ma...
...{f_\ensuremath{\mathrm{IFtuned}}^{\ensuremath{\mathrm{obs}}}}.
\end{displaymath} (24)

In the rest (source) frame, the following relations hold
\begin{displaymath}
\frac{\ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensur...
...{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}{}.
\end{displaymath} (25)

The side band separation in the rest frame is defined as
\begin{displaymath}
\ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\ma...
...h{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{rest}}}} \right] }.
\end{displaymath} (26)

It is then straightforward to show that
\begin{displaymath}
\ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\ma...
...uremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} \right] },
\end{displaymath} (27)

and
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremat...
...remath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} \right] }}.
\end{displaymath} (28)


next up previous contents
Next: Earth movements Up: Heterodyne receivers and signal/image Previous: Signal and image frequency   Contents
Gildas manager 2023-06-01