Downfiring subs on carpet?

I have a short pile rug under my entire setup.

Polyester or wool?

I recommend installing one of these Auralex Acoustics SubDude Subwoofer Acoustic Isolation Platform underneath your sub. Very effective in reducing floor borne vibrations and helps tighten the bass. 

https://www.amazon.com/gp/product/B00COVEJ1E/ref=ppx_yo_dt_b_asin_title_o02_s00?ie=UTF8&psc=1

It doesn't cost much to try both.  Why not compare and report back?

Jon, That's my exact thinking. Due to arrive on this coming Monday.

The floor construction matters not so much the rug.

I use subdude on my upper levels with suspended plywood floors that will vibrate and muddy up the bass and obscure the midrange with most any sub. I also use them there under my bottom ported Ohm Walsh speakers for same reason.  

In basement with solid concrete floor foundation and dense but thin carpet and pad, not needed.