Improving S/N by Integrating Daily Runs

In order to gain a better S/N, up to this point the data has been analysed using 64 FFT bins, resulting in about 8 km/s bin resolution. The plot is the summation of many FFT results. For 64 bins, 64 data samples are used, so for a data run of 5.37 x 109 samples, nearly 84 million FFT results are summed - provided almost 40 dB S/N improvement over a single FFT result.

It should be noted that the antenna system is a fixed position drift-scan configuration. Only 40 minutes of data can be collected each day as the target passes through the antenna beamwidth. Other systems which have tracking ability can sit right on the nose of the target for perhaps several hours and so get a better S/N in one data run than is possible here.

Although 64 FFT bins provide a good improvement to S/N, a problem arises if there are RFI spikes in the result which have not been cancelled out by the 'dark frame'. The energy of such an RFI spike is spread too far across the velocity scale because of the coarse resolution and so cannot be easily filtered out without distorting the true shape of the plot.

To improve the velocity resolution, the number of bins can be increased. For the exercise here described, the number of FFT bins has been increased to 512 - a factor of 8 w.r.t. the original 64 bins. However, this results in the number of FFT results summed being reduced by a factor of 8, with the resultant loss in S/N.

Integrating Daily Runs

To recover the loss in S/N caused by using 512 FFT bins instead of 64 FFT bins, results from successive days can be summed. This is because the day-to-day variation in doppler shift for the LMC is small and so successive days' velocity results line up with each other. This may not be the case for other targets (e.g., the SMC shows much greater variation in VLSR - hence doppler shift - over time).

The plot of summing 7 days' results is shown on the right which largely regains the loss in S/N - but now has the resolution to see narrow RFI spikes.

Although many RFI spikes have been cancelled out, it is not a perfect process, as can be seen.

Effect of Mismatch in RFI Patterns

The plot shows the effect of a mismatch between the RFI pattern in the 'dark frame' and the target data. The negative RFI spike in the bottom left-hand corner is the result of RFI which is present in the 'dark frame', but not in the target data. Consequently the 'dark frame' applies a cancellation to a non-existent RFI spike in the target data - causing a negative spike in the results.

The other RFI spike near the peak of the plot is the result of an RFI spike in the target data not matched by a spike in the 'dark frame', and so it is not cancelled out.

Some means of mitigating against these effects would improve the quality of the result plots. Some attempts to pursue this path are described in the next section.