# 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:
• Uniform
• Hann (a.k.a. Hanning)
• Hamming
• Welch
• Bartlett
• Blackman
• Blackman_Harris

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):

-- ToddHunter - 2011-04-05
Topic attachments
I Attachment Action Size Date Who Comment
png compareHanning.png manage 100 K 2014-08-15 - 15:24 ToddHunter result of au.compareHanning(npts=30000,bw=300,noise=0.5,ylimits=[-10,3000],xlimits=[45,80],denominator=0.025)
pdf ict-4034_hanning1.pdf manage 215 K 2019-03-11 - 11:28 ToddHunter ACA profile synthesis of Hanning response
pdf Note_on_Spectral_Response_V2.pdf manage 202 K 2016-04-07 - 18:10 ToddHunter
pdf Note_on_Spectral_Response.pdf manage 156 K 2014-02-23 - 12:35 ToddHunter Richard Hills' note from April 2012
png OTscreenshot.png manage 77 K 2011-04-05 - 13:42 ToddHunter
ref windowFunctions.ref manage 72 K 2014-08-15 - 11:08 ToddHunter file from CSV-494
png windows.png manage 86 K 2011-04-05 - 13:38 ToddHunter plot of window functions
Topic revision: r14 - 2019-03-11, ToddHunter
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