Aliasing

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We are keeping it accessible for historical reasons only.

General description

The hardware used to convert the digital signals from the EVLA antennas into analog signals to be fed into the VLA correlator causes power to be aliased into the bottom 0.5 MHz of baseband. This affects all sources with continuum emission, most notably, commonly-used gain calibrators. The aliased power is strongest at the very bottom of baseband, and decreases away from baseband. For all bands except X and U band on the VLA, the bottom of baseband is at low-numbered channels. For X and U band, the bottom of baseband occurs at high-numbered channels. This problem obviously affects the narrowest observing bandwidths the most, with bandwidth codes 6 (781 kHz total bandwidth, typically the narrowest commonly used on the VLA) and higher being affected over the full width of the band. Although we are investigating ways to mitigate this problem, it is likely that the effect will remain with us until the new EVLA correlator comes online. In fact, the problem will affect more and more baselines as more VLA antennas are retrofitted to EVLA antennas. Note that since the aliased signal does not correlate on VLA-EVLA baselines, only EVLA-EVLA baselines are affected.

This is illustrated in Figure 1 which shows the response across the band for two baselines; one with antennas 1 and 13 (EVLA - EVLA) and one with antenna 6 and 13 (VLA - EVLA). This example is at L-band, but it occurs at any band. In this case, the contribution of the aliasing is negative: the signal increases with increasing frequency to reach a constant level after 0.5 MHz. For other baselines, the effect can be positive, where the signal decreases with increasing frequency to reach a constant level after 0.5 MHz.

Figure 1: Response across a 0.78 MHz band for an EVLA - EVLA (antennas 1 and 13) baseline (top) and a VLA - EVLA (antennas 6 and 13) baseline (bottom).

Impact on observing

A necessary condition for aliasing to occur is that there be emission between 0 and 0.5 MHz below the bottom of baseband. This is generally the case for continuum emission but rarely so for line emission. Nonetheless, aliasing has the following consequences:

• Whereas the actual line emission may not suffer from aliasing directly, the phase and bandpass calibrators are continuum sources, and will therefore be affected over the first 0.5 MHz above baseband (or last 0.5 MHz below baseband for X band). We distinguish the following two cases:

   

  1. After excluding the affected 0.5 MHz, there still is sufficient bandwidth available to form a continuum for calibration purposes.

     In that case, form a new 'channel 0' by running the AIPS task AVSPC on the spectral line data, while making sure to exclude the affected 0.5 MHz. Use this new 'channel 0' as input for calibration tasks such as CALIB and CLCAL.

  2. After excluding the affected 0.5 MHz, there isn't sufficient bandwidth available to form a continuum for calibration purposes.

     In that case, all data from EVLA-EVLA baselines must be ignored during calibration. This can be done by flagging all EVLA-EVLA baselines prior to calibration, e.g. by using UVFLG with OPCODE='FLAG' and a unique choice for the adverb REASON. Note that in this way EVLA antenna gains are still being determined, but based on VLA-EVLA baselines only. After the full calibration (including bandpass) is complete, the EVLA-EVLA baselines need to be unflagged, again using UVFLG, now with OPCODE='UFLG', and the same value of REASON as was used when flagging them.

     For subarrays containing only EVLA antennas the above will clearly not work, and methods for calibrating these data are under investigation.

• In most cases, the field of view will contain both line and continuum emission, and removing the continuum requires extra care.

  The aliased continuum can be subtracted in the visibility plane using the AIPS task UVLSF, just as has been common practice in the past for data not affected by aliasing. However, in order to fit the shape of the aliased continuum, a high order fit is needed. The latest version of UVLSF now supports orders up to 4, and users will need to make sure they have run a Midnight Job since October 31, 2007, to obtain this version. It is our experience that a fourth order fit is required and sufficient to properly represent the aliased continuum. Note that while the line signal can be recovered this way, this is not the case for the continuum as there is no way to separate the aliased part of the continuum from the unaffected part. We have received reports, though, that running BLCAL can improve the resulting continuum, but this requires frequent observations of a strong calibrator.

  Clearly, a higher order polynomial fit will only work if there is a sufficient number of line-free channels at either end to base the fit on. We recommend that at least one-quarter of the total bandwidth at either end is line-free. In other words, the total number of channels with line emission should not exceed 50% of the total number of channels.

  A successful fit requires aliased signal to base the fit on. This may not be the case if the field of view does not contain strong continuum sources. We are considering implementing AIPS software that will perform the UVLSF fit on calibrators only, and subtract a properly scaled version of this aliased response from the source data. In anticipation of such a task, we strongly recommend all spectral line observers planning to use narrow bandwidths to give higher weight to strength than to vicinity to the source, when deciding which phase calibrator to use.

  Note that it is almost certainly impossible to stitch together narrow bands to obtain wider frequency/velocity coverage for wide spectral lines, because there is no way to subtract the aliased continuum signal in this case. Also, the line emission below baseband will be aliased into the band in an unpredictable way depending on the shape and strength of the emission line.

• In all cases, noise is aliased into the band and will decrease the effective sensitivity, with the channels closest to baseband being the most affected

Typical cases

Bandstitching

Bandstitching is the technique using IFs partially overlapping in frequency, e.g.:

        IF A   |----------------------|
        IF B                   |----------------------|
                         ^^^^^^^
        

What can be done in post-processing

A new task FIXAL has been added to AIPS which fits observations of calibrator sources to determine the aliasing function and then fits that function to line-free channels in the main data set to determine alias-free amplitude and phase, and to correct the data for the aliasing. A procedure FXALIAS was written to assist in the operation. It runs BPASS using only VLA-VLA and VLA-EVLA baselines, applies the bandpass to all data with SPLAT, separates the bandpass calibrators with UVCOP, and then runs FIXAL. Note that this operation must be done on totally uncalibrated data: if any phase correction has been applied, the above formula will have been rendered incorrect.

At present, the new task and procedure should be regarded as highly experimental. They appear to work most of the time and to remove most of the problem. There are niggling bits left and there are cases in which they do not work well. In general we recommend observers to plan their observations in such a way (i.e. not needing the aliased part of the spectrum in any post-processing) that they do not have to rely on post-processing to get rid of effects of kaliasing.
See the relevant section of the 30JUN08 AIPSLetter, and the AIPS HLP files for FXAL and FXALIAS for further details.