Filter
late Middle English (denoting a piece of felt): from French filtre, from medieval Latin filtrum ‘felt used as a filter’, of West Germanic origin and related to felt1.
wiktionary
From Middle English filtre, from Medieval Latin filtrum (compare also Old French feutre(“felt; filter”)), from Frankish *filtir, from Proto-West Germanic *felt. See felt.
etymonline
filter (n.)
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.
filter (v.)
1570s (transitive), from French filtrer or from Medieval Latin filtrare, from filtrum "felt" (see filter (n.)). The figurative sense is from 1830. Intransitive use from 1798. Related: Filtered; filtering.
