According to Wikipedia and other sources, cats do not have any unique anatomical features which make them able to produce the purring sound.

Considering that some other mammals are also known for purring (rabbits, squirrels, etc.); is it practically possible for a human to purr?

For most people yodeling, throat singing or ventriloquism seems impossible but by training the muscles in the neck inter alia, most people can learn these feats.

I guess humans can't exactly get the same sound "filter", but is learning how to dilate/constrict the glottis rapidly possible (e.g. 40Hz)?

Yes, humans can learn to purr. I had cats around meconstantly forth first 30 years of my life. Being a wierd little kid, one of the odd things I decided to try to learn was to be able to purr just like my cats. As a result, I learned to make what at least sounds like a purr and be ableto keep it up between breaths. The hard part is learning to purr while both breathing in and out. soyes, it can be done.
Sadly, this skill (?) does take practice. I have not had cats consistently with me formore than 10 years and I can no longer purr as easily as I once could.

BTW: it is a myth that large cats can not purr. Won't does not equal can't. There have been recorded instances of tigers purring on the very rare occassion. Admittedly, I have only heard of a few such instances and not with any of the other large cats, but the anatomy is not really any different from alion, so I presume they have the anatomical ability, just not the instinctual ability. If any others know more about this, please chime in.