This article investigates the problem of nonfragile filter design for discrete-time linear systems subject to noises with known frequency ranges. Additive interval uncertainty reflecting imprecision in filter implementation is considered. By the aid of generalised KYP lemma, both deterministic and randomised filtering algorithms are proposed to deal with noises in low-, middle- and high-frequency domain, respectively. The proposed nonfragile finite-frequency filters can get a better noise attenuation performance when frequency ranges of noises are known beforehand. An example about F-18 aircraft model is given to illustrate the effectiveness of the proposed algorithms.