1610s, probably a back-formation from filtration or else from Medieval Latin filtratus, from filtrum "felt" (see filter (n.)). Related: Filtrated; filtrating. As a noun, "liquid which has passed through a filter," from 1846.
early 15c., "piece of felt through which liquid is strained," from Old French feutre "felt, felt hat, carpet" (Modern French filtre) and directly from Medieval Latin filtrum "felt" (used to strain impurities from liquid), from West Germanic *filtiz (from PIE root *pel- (5) "to thrust, strike, drive"). Figurative use from c. 1600. As a pad of absorbent material attached to a cigarette, from 1908.