Targeted searches of continuous waves from spinning neutron stars normallyassume that the frequency of the gravitational wave signal is at a given knownratio with respect to the rotational frequency of the source, e.g. twice for anasymmetric neutron star rotating around a principal axis of inertia. In factthis assumption may well be invalid if, for instance, the gravitational wavesignal is due to a solid core rotating at a slightly different rate withrespect to the star crust. In this paper we present a method for {\itnarrow-band} searches of continuous gravitational wave signals from knownpulsars in the data of interferometric detectors. This method assumes sourceposition is known to high accuracy, while a small frequency and spin-down rangearound the electromagnetic-inferred values is explored. Barycentric andspin-down corrections are done with an efficient time-domain procedure.Sensitivity and computational efficiency estimates are given and results oftests done using simulated data are also discussed.
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