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Handling Dual-Sideband Spectra

Dual sideband super-heterodyne receivers produce spectra in which each channel contains contributions from two different frequencies, referred to as the ``upper sideband frequency'' and the ``lower sideband frequency''. In the rest frame of the observer (topocentric), these are related to each other as follows:


\begin{displaymath}
f_{lsb} = 2.f_{LO} - f_{usb}
\end{displaymath} (1)

where $f_{LO}$ is a fixed frequency known as the ``local oscillator frequency''. In other words, the local oscillator frequency is always mid-way between any pair of corresponding upper and lower sideband frequencies15. If you want to describe the spectral axis of such a spectrum using a SpecFrame you must choose whether you want the SpecFrame to describe $f_{lsb}$ or $f_{usb}$ - a basic SpecFrame cannot describe both sidebands simultaneously. However, there is a sub-class of SpecFrame, called DSBSpecFrame, which overcomes this difficulty.

A DSBSpecFrame has a SideBand attribute which indicates if the DSBSpecFrame is currently being used to describe the upper or lower sideband spectral axis. The value of this attribute can be changed at any time. If you use the AST_CONVERT function to find the Mapping between two DSBSpecFrames, the setting for the two SideBand attributes will be taken into account. Thus, if you take a copy of a DSBSpecFrame, toggle its SideBand attribute, and then use AST_CONVERT to find a Mapping from the original to the modified copy, the resulting Mapping will be of the form of equation [*] (if the DSBSpecFrame has its StdOfRest attribute set to ``Topocentric'').

In general, when finding a Mapping between two arbitrary DSBSpecFrames, the total Mapping is made of of three parts in series:

  1. A Mapping which converts the first DSBSpecFrame into its upper sideband representation. If the DSBSpecFrame already represents its upper sideband, this Mapping will be a UnitMap.
  2. A Mapping which converts from the first to the second DSBSpecFrame, treating them as if they were both basic SpecFrames. This takes account of any difference in units, standard of rest, system, etc between the two DSBSpecFrames.
  3. A Mapping which converts the second DSBSpecFrame from its upper sideband representation to its current sideband. If the DSBSpecFrame currently represents its upper sideband, this Mapping will be a UnitMap.

If an attempt is made to find the Mapping between a DSBSpecFrame and a basic SpecFrame, then the DSBSpecFrame will be treated like a basic SpecFrame. In other words, the returned Mapping will not be affected by the setting of the SideBand attribute (or any of the other attributes specific to the DSBSpecFrame class).

In practice, the local oscillator frequency for a dual sideband instrument may not be easily available to an observer. Instead, it is common practice to specify the spectral position of some central feature in the observation (commonly the centre of the instrument passband), together with an ``intermediate frequency''. Together, these two values allow the local oscillator frequency to be determined. The intermediate frequency is the difference between the topocentric frequency at the central spectral position and the topocentric frequency of the local oscillator. So:


\begin{displaymath}
f_{LO} = f_{central} + f_{if}
\end{displaymath} (2)

The DSBSpecFrame class uses the DSBCentre attribute to specify the central spectral position ($f_{central}$), and the IF attribute to specify the intermediate frequency ($f_{if}$). The DSBCentre value is given and returned in the spectral system described by the DSBSpecFrame (thus you do not need to calculate the corresponding topocentric frequency yourself - this will be done automatically by the DSBSpecFrame when you assign a new value to the DSBCentre attribute). The value assigned to the IF attribute should always be a topocentric frequency in units of Hz, however a negative value may be given to indicate that the DSBCentre value is in the upper sideband (that is, if $IF < 0$ then $f_{central} > f_{LO}$). A positive value for IF indicates that the DSBCentre value is in the lower sideband (that is, if $IF > 0$ then $f_{central} < f_{LO}$).



next up previous 264
Next: Time Systems (TimeFrames)
Up: Spectral Coordinate Systems (SpecFrames)
Previous: Creating Spectral Cubes

AST A Library for Handling World Coordinate Systems in Astronomy
Starlink User Note 210
R.F. Warren-Smith & D.S. Berry
24th May 2011
E-mail:ussc@star.rl.ac.uk

Copyright (C) 2009 Science \& Technology Facilities Council