'bandlimited' originates from English, specifically the combination of 'band' and 'limit', where 'band' meant 'a strip or zone' and 'limit' meant 'boundary'.

'band' comes from Old Norse 'band' meaning 'a binding or strip', and 'limit' comes from Latin 'limes' (boundary) via Old French; the adjectival/past-participle form 'limited' is formed with the English suffix '-ed', and the compound 'band-limited' arose in technical usage (20th century) to describe frequency-restricted signals.

Initially the components referred to a physical 'band' and a 'boundary'; in technical contexts (especially signal processing) it evolved to mean 'restricted in frequency content' or 'having no energy outside a specified frequency band'.