It’s Harry Nyquist, from engineering and signal theory 
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I think that quote is a bit misleading. As the author of the page shows the Lanczos method does a good job without the need for any pre filtering yet it is doing discrete sampling on a regular grid.
The issue the author appears to be having is that the version of Photoshop out at the time did not support Lanczos resampling.
Regards, Freddie.
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The Lanczos method is shown for ImageMagick with the comment that:
Finally I’ll give an overview of some of the standard sampling filters of ImageMagick™,combined with the anti-aliased resizing provided by it.
Meaning that the ImageMagick examples had anti-aliasing applied and those are the only examples that include Lanczos. So the quote is not misleading but perhaps is open to interpretation.
I mean you can try it for yourself. Take the Rings1.png image you posted and run:
magick Rings1.png -filter Lanczos -resize 200x nrings.png
and you’ll get:
Observe how there is no pre-filtering or any other weirdness; just straight Lanzcos.
Regards, Freddie.
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Oops, I misunderstood your “pre-filtering” so now I agree, thanks for the clarification.
Best, Ted.
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Yes, Lanzcos is the anti-aliasing. Use a Lanzcos filter and you get a mostly aliasing free result. It isn’t perfect so far as aliasing goes but for a variety of reasons you often don’t want perfect. (Perfect would be a sinc filter but they are prone to oscillations and have other undesirable quirks.)
Regards, Freddie.