Etymology
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Words related to filter

*pel- (5)
Proto-Indo-European root meaning "to thrust, strike, drive."

It forms all or part of: anvil; appeal; catapult; compel; dispel; expel; felt (n.) "unwoven fabric matted together by rolling or beating;" filter; filtrate; impel; impulse; interpellation; interpolate; peal; pelt (v.) "to strike (with something);" polish; propel; pulsate; pulsation; pulse (n.1) "a throb, a beat;" push; rappel; repeal; repel; repousse.

It is the hypothetical source of/evidence for its existence is provided by: Greek pallein "to wield, brandish, swing," pelemizein "to shake, cause to tremble;" Latin pellere "to push, drive;" Old Church Slavonic plŭstĭ.
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filtration (n.)
"act or process of filtering," c. 1600, perhaps from French filtration (1570s), noun of action from filter "to filter" (see filter (v.)).
felt (n.)
unwoven fabric matted together by rolling or beating while wet, Old English felt "felt," from West Germanic *feltaz "something beaten, compressed wool" (source also of Old Saxon filt, Middle Dutch vilt, Old High German filz, German Filz, Danish filt), from Proto-Germanic *felt- "to beat," from PIE root *pel- (5) "to thrust, strike, drive," with a sense of "beating." Compare filter (n.). Felt-tipped pen (or -tip) is from 1953.
filtrate (v.)
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.