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Palpatine was using Force concealment. I think somebody of his calibre of Force would require a substantial amount of Force just to use that.
Since Yoda is the oh-so-hallowed being of wisdom and Force skill they make him out to me, wouldn’t he detect this level of Force? Why didn’t he sense the Chancellor, at least in visions as he slept or in meditation if not consciously?
The whole point/purpose/effect of Force Stealth is specifically to hide one's Force signature. The Jedi could not detect that Palpatine was using Force Stealth, simply because he was using Force Stealth.
From Wookieepedia:
Force stealth also referred to as Force Concealment or Buried Presence was a power that was used by highly skilled Force-sensitives to mask their Force alignment (Light or Dark), their ability to use the Force, or even their entire presence from other Force-sensitives.
One could, however, argue that their inability to detect him was in part, due to the Jedi's diminished ability to use The Force as mentioned in Attack Of The Clones.
Windu: I think it is time we informed the Senate that our ability to use the Force has diminished.
Yoda: Only the Dark Lords of the Sith know of our weakness. If informed, the Senate is, multiply, our adversaries will.
There is a great answer explaining why the Jedi's ability is diminished on the question How did Darth Sidious manage to diminish all of the Jedi's ability to use the Force?
See also: Why couldn't the Jedi detect Senator Palpatine as having powers?
Exerting force energy by using the force to conceal force energy sounds illogical. The reason Yoda couldn't tell was because all of Palpatine's force power was concealed, yes, even during sleep and meditation.
