Todah hdwt from the root hdy is most often translated as "thanksgiving". It is a noun formed from the Hiphil of hdy ydh which can have two meanings. The more frequent meaning is "to give thanks, lauds and praise"; the less frequent meaning is to confess, either the name of God or one's sin:
My sins I made known to you
my iniquity I did not hide.
I said: "I will confess (hdwa 'odeh) to Yahweh"
and you took away the guilt of my sin (Psalm 32:5)
He who conceals his sins prospers not
but he who confesses and forsakes them
obtains mercy (Prov. 28:13)
As a noun, "todah" appears some 29 times. It is clear from Leviticus 7 (12, 13,15) that it is a type of a peace offering, i.e., a partially burnt offering, the flesh of which can be eaten. But in Jos. 7:19, the context demands that it be given the meaning of "confession of sin."
And Joshua said to Acan, son of Simna: "Give glory to Yahweh, God of Israel, and give him todah. Tell me what you have done; do not hide anything from me."
And Acan answered Joshua: "Yes, I sinned against Yahweh the God of Israel. This is what I did..." (Joshua 7:19-20)
The question is whether "todah" as used in Psalm 50 is better rendered "confession of sin" rather than "thanksgiving." The noun appears twice in Psalm 50 as an object of the verb xbz zbh in verses 14 and 23
Sacrifice to God todah
fulfill your vows to Elyon (v. 14)
He who sacrifices todah honors me (v. 23)
Our modern English translations consistently translate "todah" in both verses as "thanksgiving." However, the translation makes no sense seen from the contents of the psalm.
Psalm 50 is not an ordinary psalm since it isn't designed as a prayer. It looks more like a lawsuit discourse (a byr rib) where God comes to accuse his people of sin. In the first part of the discourse, God, the plaintiff and judge makes a negative definition of the complaint: it is not about sacrifices (v. 
because the sacrifices offered mean nothing to him anyway (vv.9-13). So instead, he says: "Sacrifice to God todah"
The meaning of todah becomes clearer in the second part of the discourse where the complaint is defined positively. Here, the "people" in v. 7 have become the "wicked" (v.16): these pay lip service to the Law (vv. 16-17) and they connive with thieves and adulterers (v., they lie and slander (vv. 19-20). Much worse, they think that in all these, God is a silent partner (v. 21). But now God ceases to be silent: "I now accuse you and lay the charge against you." (v. 21b)
Considering that the above is an accusation, would it still be possible to think of todah as a thanksgiving offering that God wants in this instance? A thanksgiving sacrifice at this point in the accussation would be imcomprehensible. Wouldn't it be more fitting to understand todah here as an admission of guilt or a confession of sin? I think that this second one is the better alternative.
