Reduction of frequency-switched data

For observations taken in frequency-switched mode, the `raw' spectrum consists of two copies of the line profile displaced in both plus and minus frequency directions from the nominal line position by an amount equal to the frequency switch employed. This situation is shown in the top part (`original') of the schematic below. Here the nominal line position (at the centre of the spectrometer window) is indicated by `+' and the frequency switch offset by `fsw'. There is a positive offset in the signal phase, and a negative one in the reference phase. The spectrum thus has both positive- and negative-going features (`+L' and `-L' respectively) corresponding to the two phases.

The data reduction of such a spectrum is done by `shifting and adding': copies of the spectrum are shifted in frequency by plus and minus the frequency-switch amount, and then subtracted. The result is divided by 2 to form the end result, as shown below schematically:

The final spectrum consists of the line at the correct frequency (and velocity) and two half-height negative `ghost' images of the line (at `G' in the plots above). The separation of the ghosts from the line is $\pm2.0\Delta\nu$, where $\Delta\nu$ is the original frequency-switch. Any offset and/or slope in the spectrum is automatically removed by this step, but curved baselines are not. A `real-life' example of the above process is shown in Figure .

Figure: A portion of the `raw' frequency-switched spectrum of the CO(2-1) emission towards L1498 appears at the bottom of this panel. A linear baseline was subtracted for clarity. At the top is the `shifted and subtracted' spectrum. The final CO line profile is at the middle (V$\sim 8$ km/s), flanked by negative-going `ghost' images. The left-hand one of the latter coincides with a `ghost' image from telluric CO, off the frame to the left.

In practice one can expect a slowly-varying (and sometime large amplitude) sinewave across the band when observing in a frequency-switched mode. It may therefore be necessary to subtract higher-order polynomials from the baseline than with position- or beam-switching. In addition strong interference spikes can appear in the band, particularly when using A2. In other observing modes these will be largely cancelled out, but in the frequency-switched mode any such spike has the opportunity to appear twice. Such spikes may be accompanied by `ringing' as a result of the Fourier transform applied to the data by the DAS. These problems should be taken into account during the data reduction.

Practical data reduction therefore consists of the following steps, some of which may be optional:

• Average all equivalent spectra together.
• If using more than one subband with the DAS merge the subbands together using the SPECX command das-merge. This step will not be needed if the spectra are taken with the AOSC.
• Apply Hanning smoothing to the spectrum if there is clear `ringing' associated with spikes in the band.
• Remove interference spikes using e.g. rem-spike or set-chann in SPECX.
• There is a special procedure (fsw) to do the shifting and adding; it needs to be provided with the frequency shift you used during the observing; e.g. type:

  >> fsw 8.1

  In this case the frequency switch was $\pm8.1$ MHz.

  This takes the contents of the x-register (assumed here to be the result of the previous steps listed above) and replaces it with the shifted-and-averaged version. As noted within the procedure you may be asked to provide a frequency; this is the result of a software workaround for `slow-frequency switching' (using receivers A2 and C2). To find out the frequency run SPECSUM and note the rest frequency given there for the data in question.

• Any residual baselines can now be removed with a polynomial (use f-p-b in SPECX) or composite (polynomial and sinusoidal; use f-c-b) function.
• Save the final result, once you are happy; you won't want to do all this again.