[evlatests] aliasing, time variability

[Barry Clark]

The theoretical law, and I would be astounded if it were not closely followed, 
is that the complex amplitude in channel n is  
1+a*exp(2*i*pi*(2*n-1)*W*w)
Where W is the channel width, in, say, Mhz
w is the usual w expressed in, say, microseconds
a is a channel dependent constant that I'm sure Mike Revnell could supply,
being the ratio of the transmission at f0-(n-0.5)*W to that at f0+(n-0.5)*W.

Remember, this law is only for EVLA-EVLA baselines, and only for continuum 
radiation - the effect usually vanishes for the line case.  It is a grave
error to include EVLA-EVLA baselines in a bandpass calibration except in
the case where the line radiation is small compared to the continuum.

No bets accepted about whether it is 2*i*pi or -2*i*pi.

I think the way to proceed is to print out some w's and see what is 
expected.  Then, only if you are feeling exceptionally strong, look and see 
if the data deviates from the above law.

> From evlatests-bounces at donar.cv.nrao.edu  Tue Oct 23 14:54:30 2007
> Date: Tue, 23 Oct 2007 14:53:48 -0600
> From: Gustaaf van Moorsel <gvanmoor at nrao.edu>
> 
> This is a first report on the time variability of the aliasing dis-
> covered recently in narrow-band spectral line observations.  The
> observations presented here are 12 consecutive scans on 0137+331 for
> a total of 3 hours, BW code=5, mode 2AC, for a total of 256 channels
> and 1.5 MHz bandwidth, all at L-band.
> 
> The problem is easily seen on EVLA - EVLA baselines; to illustrate
> this I have attached POSSM1316.pdf showing the excess amplitude in
> the first 100 channels (0.6 MHz) on baseline 13 - 16.  This is an
> average over the full 3 hours; in the following I investigate the
> time dependeny of the effect.
> 
> Continuing to limit myself to baseline 13 - 16, I determined the
> average amplitude for each 15 minute scan in 6 adjacent 0.12 MHz
> (20 channels) wide frequency intervals.  In other words, the prev-
> ious plot is broken up in chunks of time (scans) and frequency.
> 
> The results are shown in the attached file aliasing.pdf.  The legend
> on the right is in units of MHz, so the top (blue) points show the
> average amplitude around 0.14 MHz (the average of channels 13 - 32)
> as a function of time in minutes.  The next - pink - points show the
> average amplitude around 0.26 MHz (the average of channels 33 - 52),
> etc.
> 
> The result is that apart from a dip at 80 minutes, the amplitudes are
> largely constant.  Next on my list is to check the phase behavior at
> 80 minutes.  Obviously, this result is for one baseline only - I int-
> end to check out one or two other EVLA - EVLA baselines as well.
> 
> Comments and suggestions welcome!
> 
> Gustaaf
> 
> 
>