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The discussion of Section 1.3.1 is still valid for
both the signal and image frequency axes. Eq. 14 can easily be
rewritten
 |
(60) |
and
 |
(61) |
with
 |
(62) |
is simply the tuning frequency entered by the user.
However,
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}](img132.png) |
(63) |
It is straightfoward to show that it is constant and equal to
 |
(64) |
In the rest (source) frame, the following relations hold
 |
(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}](img135.png) |
(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}](img136.png) |
(67) |
and
![\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{...
...remath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} \right] }}.
\end{displaymath}](img137.png) |
(68) |
Next: Earth movements
Up: Heterodyne receivers and signal/image
Previous: Signal and image frequency
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Gildas manager
2015-03-19