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Signal and image frequency axes in the rest frame

The discussion of Section 1.3.1 is still valid for both the signal and image frequency axes. Eq. 14 can easily be rewritten

\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{sig}}^{\ensuremath{\mathr...
...emath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath} (60)

and
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{ima}}^{\ensuremath{\mathr...
...emath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath} (61)

with
\begin{displaymath}
\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\e...
...athrm{sys}}}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}.
\end{displaymath} (62)

\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} (63)

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} (64)

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} (65)

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} (66)

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} (67)

and
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{...
...remath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} \right] }}.
\end{displaymath} (68)


next up previous contents
Next: Earth movements Up: Heterodyne receivers and signal/image Previous: Signal and image frequency   Contents
Gildas manager 2015-03-01