Banks of templates for directed searches of gravitational waves from spinning neutron stars

We construct efficient banks of templates suitable for directed searches of almost monochromatic gravitational waves originating from spinning neutron stars in our Galaxy in data being collected by currently operating interferometric detectors. We thus assume that the position of the gravitational-wave source in the sky is known, but we do not assume that the wave's frequency and its derivatives are a priori known. In the construction we employ a simplified model of the signal with constant amplitude and phase which is a polynomial function of time. All our template banks enable usage of the fast Fourier transform algorithm in the computation of the maximum-likelihood F-statistic for nodes of the grids defining the bank. We study and employ the dependence of the grid's construction on the choice of the position of the observational interval with respect to the origin of time axis. We also study the usage of the fast Fourier transform algorithms with nonstandard frequency resolutions achieved by zero padding or folding the data. In the case of the gravitational-wave signal with one spin-down parameter included we have found grids with covering thicknesses which are only 0.1-16% larger than the thickness of the optimal 2-dimensional hexagonal covering.