ALMA Correlator Window Functions
The ALMA correlator can apply a variety of window functions
to the time domain data. These are selectable in Phase 2 of the Observing Tool, as shown in the thumbnail snapshot below:
Here is the list:
- Hann (a.k.a. Hanning)
The actual functions used are available in text format in CSV-494
by Rodrigo Amestica (and attached to this wikipage). Here is a plot
. The expected FWHM (i.e. spectral resolution) and effective channel bandwidth of each of these modes in terms of number of channels is given in Richard Hills' note from May 2012
. Todd tested Richard's values on real ALMA data, summarized here
The documentation of the casa hanningsmooth task is here
A good reference for window functions is Harris 1978
, but note that it uses the engineering definition of effective noise bandwidth, which is only 1.5 channels for the Hann window (alpha = 2), rather than 8/3 in the astronomical correlator case. Also, note that it is the 6-dB bandwidth (power = amplitude squared) in his Table 1 that gives the effective resolution (not the 3-dB bandwidth).
The following is a plot I made in order to answer a Helpdesk question (which became a Knowledgebase article
) on the equivalence of time domain vs. frequency domain Hanning smoothing. The underlying relation between the methods are discussed on this Wolfram page
. The general mathematical proof is also in Appendix A of Harris 1978 (see above).
- result of au.compareHanning(npts=30000,bw=300,noise=0.5,ylimits=[-10,3000],xlimits=[45,80],denominator=0.025):