Spatial PFB

[jdbowman]

I've been thinking about how to fold in long baselines for better resolution (and not to waste information), especially for when we add a node to OVRO-LWA. We don't have the resources in the GPU to expand our image/aperture grids, but we could borrow a technique from software implementations of polyphase filter banks (PFBs). In 1D, PFBs apply a sync window function to a long array of data and then cut apart the long array into shorter segments, co-add/stack the segments, and FFT the short-length array. This improves the PSF compared to doing FFTs on individual unweighted short segments of data (at the expense of less sensitivity since some of the data is down weighted by the sync window function--that loss of sensitivity can be regained by sliding the PFB along the original array, although that won't apply here). I think we could do that spatially (in 2D) with our aperture planes, essentially weight and fold outlier antennas back into the central part of the aperture before we FFT. We can't do better than our maximum grid dimension for imaging resolution, but we can shrink the PSF closer to the size of a pixel in the image domain and reduce sidelobes. A simple test in simulation would be a good start and possible a nice quick paper.

[infinitron]

Here is a short simulation that I made to demonstrate a 2D PFB. I multiply a 96x96 grid (with a resolution of 1 deg, for example) with a 2D sinc filter. I then divide it into nine 32x32 grids (our allowed grid size) and accumulate them to perform FFT. This is essentially folding through the edges. The resulting PSF is compressed into a single pixel compared to the one generated using the 96x96 grid. But I'm a little confused about the resolution. Does the sky resolution remain the same between larger and smaller grid sizes? Or does the smaller grid have a 3x lower resolution than the full grid. Also, how do we ensure we conserve the flux after we down-weight the outlying antennas?

[jdbowman]

The simulation looks good. The resolution for the PFB case should match the low-resolution case, but with lower sidelobs. I think your example simulation looks like the right outcome. So for example, when we deploy on OVRO-LWA, which has a core diameter of ~200 meters (instead of 100 meters like LWA-SV) and about 100 outrigger antennas even farther away (a couple km) , we wouldn't be able to make an aperture grid big enough to include all those more distant antennas. Using the same size aperture grid as we do for LWA-SV, this method would let us at least keep some of that information by folding it back in and use it to help reduce the sidelobes of our PSF compared to ignoring that data completely.

[jdbowman]

Nivedita or Katherine could get you the positions of all the OVRO-LWA antennas and we could run a similar simulation for that specific case, using the LWA-SV grid settings plus the PFB folding for more distant antennas.

Regarding the flux question, since the sinc weighting function is known, I think it can be accounted for in the normalization of the output.