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I agree that correlations are important. Correlated outputs will
probably be the default mode for most PAF observations, and real
time beams would only be used when phase information is important,
such as for pulsar surveys (can pulsar searches be done with fine
grained, narrowband correlations?) <br>
<br>
I'm not sure whether the bandwidth issue is the real driver. Real
time beams also have to be formed in subbands and then either
processed for pulsar surveys or integrated for power spectra. I
don't think bandwidth is really what drives the difference between a
B engine and an X engine. It's true that if one only forms a few PAF
beams, then with a given disk storage data rate one could store the
beam outputs over finer frequency subbands than correlations, but if
fully sampled beams are formed, the data rate wouldn't be very
different between beam outputs and correlations with the same
integration time and frequency resolution. Am I missing something?<br>
<br>
There is another motivation for beamformers in the broader PAF
community, and that is for synthesis arrays. The correlator for the
dish array is expensive, so one would only want to correlate as
small a number of beams from each PAF as possible. This raises a
question - could correlations from each PAF be used to get
correlations of the dish array somehow? Is there an efficient
two-level correlator architecture, with a PAF correlator for each
dish, followed by the synthesis array correlator? I suspect not, but
I can't quite convince myself. In any case, it seems that for single
dish telescopes, there's less motivation to use a beamformer back
end instead of a correlator.<br>
<br>
Finally, there is probably a bit of analysis one could to to show
how closely beams must be spaced in order for the information in the
beams to be equivalent to the correlations. It's essentially the
problem of recovering the matrix R from a set of inner products
w'*R*w for many vectors w. I suspect that if one forms HPBW/2 spaced
beams over the PAF FoV, the information in the beams is less than
but on the order of the information in R in some quantiable sense.
Information in the deep sidelobes is lost, but most of the large
eigenvalues of R represent sources in the field of view. With finer
beams, even just over the PAF field of view, all information even
out in deep sidelobes could well be contained in the beam outputs,
but that's a moot point, as one would not form that many beams in
practice. There's also the idea of eigenbeams proposed by Cornwell
et al., so that one can form very few PAF beams yet still have
information over the full field of view.<br>
<br>
Karl<br>
<br>
<br>
<div class="moz-cite-prefix">On 5/20/2013 9:25 AM, Brian Jeffs
wrote:<br>
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Rick,
<div><br>
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<div>I agree that you have much more flexibility to try different
beamformer designs, detection algorithms, interference
mitigation techniques, superresolution, calibration correction,
etc. if you store and operate on the accumulated cross products
(correlation matrices). However, you give up the ability to do
fine resolution spectral processing. You are stuck with the
coarseness of the correlator's frequency channelization. I
don't know how problematic this is for some applications, such
as pulsar searches, where fine spectral resolution may be
needed.</div>
<div><br>
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<div>Brian</div>
<div><br>
<div>
<div>On May 20, 2013, at 6:38 AM, Anish Roshi wrote:</div>
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Yes indeed. We can form images with beams with different
optimization if the correlations are recorded.<br>
</div>
Anish<br>
</div>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote">On Sun, May 19, 2013 at 9:57 AM,
Rick Fisher <span dir="ltr">
<<a moz-do-not-send="true"
href="mailto:rfisher@nrao.edu" target="_blank">rfisher@nrao.edu</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
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Brian, Karl,<br>
<br>
In trying to understand the ASKAP data processing
architecture, I'm<br>
beginning to understand the fundamental importance of
saving the<br>
cross-products between array element outputs in our
own PAF data<br>
processing. In forming beams you throw away a lot of
information in the<br>
array's field of view that can be recovered only by
forming many beams<br>
with very close spacing (much closer than HPBW/2).
This has important<br>
consequences for the sensitivity to point sources, as
in the search for<br>
pulsars. Hence, I would suggest that the most
important archived outputs<br>
from your signal processor are the cross-products
rather than formed<br>
beams. For a given data storage volume, there's more
information in the<br>
cross-products than in the formed beam outputs. In
some respects, the<br>
"beam" concept is a holdover from a waveguide feed
where there's only one<br>
output, and most of the information in the focal plane
is reflected back<br>
into the sky.<br>
<br>
Rick<br>
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<pre class="moz-signature" cols="72">--
Karl F. Warnick
Department of Electrical and Computer Engineering
Brigham Young University
459 Clyde Building
Provo, UT 84602
(801) 422-1732
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