[evla-sw-discuss] Residual sub-sample delay correction

[Barry Clark]

Following the general tenor of Brent's message and my response, I
think the big picture is pretty clear.  The correction is based on
the fact that the station boards handle delay tracking smoothly and
correctly for the centers of the subbands, and that for other
frequencies in the subband, one can consider that the delay changes
suddenly by one sample time when the delay commanded by the delay
polynomial crosses a half integral number of sample times.  This
sudden change in delay is the effect we want to correct.

It suffices to calculate for each integration only the first two
terms of the delay error expansion - the mean delay error over the
integration, and a decorrelation, which is, effectively, the mean
square delay error.

To do these calculations, the CBE must have available the delay
polynomials and the sample time (1/2GHz or 1/4GHz resp for 8bit
and 3 bit samplers).  So the CBE must have a listener for the
delay polynomial multicasts, and must be able to route to this
processor the sample time, the integration start time, and the
integration length, on an antenna and baseband basis.

There will be a station based (or rather subband based) process
which does the initial processing and leaves expanded results around
for efficient use by a baseline based process.  The baseline based
part will calculate the (complex) correction factor which will have
the form (1 + i*f*mean_delay_residual + f*f*decorrelation_factor),
where f is the frequency, relative to subband center, in real
frequency units, so the software that applies this factor must know
the subband bandwidth in order to convert from channel number to
frequency units.

Since the Executor does not currently support different delay
polynomials for different subbands of a single baseband, it would
be an acceptable simplification for an initial implementation to
do the calculation of mean_delay_residual and decorrelation_factor
on a baseband basis, as long as the eventual expansion to a subband
basis is kept in mind.

It should be noted that the delay polynomials are delivered on the
basis of antenna/station board, and the CBE will need to be able to
route this to the process(es) which is producing the spectrum to be
corrected.

For testing purposes, it would be nice to be able to turn the
corrections on or off without having to restart a different version
of the CBE.  A manual on/off, as opposed to one through the VCI,
should suffice for the moment.

It is my intention to produce, over the next week or so, code fragments
embodying my suggested algorithms for the station-based and baseline-
based processes.