This　paper　deals　with　the　sensor　fault　detection　problem　for　linear　time-invariant　continuous-time　systems　with　disturbances　and　sensor　noises.　Two　finite　frequency　performance　indexes　are　introduced　to　increase　the　fault　sensitivity　and　attenuate　the　effects　of　disturbances　and　noises.　Different　from　the　existing　techniques,　the　recently　developed　Generalized　Kalman-Yakubovich-Popov　(GKYP)　lemma　is　applied　in　this　paper　to　treat　the　finite　frequency　performance　indexes　directly,　completely　avoiding　the　complexity　of　weighting　functions　of　the　existing　approaches.　The　design　methods　are　presented　in　terms　of　solutions　to　a　set　of　linear　matrix　inequalities　(LMIs).　A　numerical　example　is　studied　to　illustrate　the　effectiveness　of　the　proposed　method.