We show that every analytic filter is generated by a $\Pi^0_2$ prefilter, every $\Sigma^0_2$ filter is generated by a $\Pi^0_1$ prefilter, and if $P \subseteq \mathscr{P}(\omega)$ is a $\Sigma^0_2$ prefilter then the filter generated by it is also $\Sigma^0_2$. The last result is unique for the Borel classes, as there is a $\Pi^0_2$-complete prefilter $P$ such that the filter generated by it is $\Sigma^1_1$-complete. Also, no complete coanalytic filter is generated by an analytic prefilter. The proofs use Konig's infinity lemma, a normal form theorem for monotone analytic sets, and Wadge reductions.