PLANCK : Systematic effects induced by periodic fluctuations of arbitrary shape

A fundamental requirement in the new generation of high resolution Cosmic Microwave Background imaging experiments is a strict control of systematic errors that must be kept at $\mu$K level in the final maps. Some of these errors are of celestial origin, while others will be generated by periodic fluctuations of the satellite environment. These environment instabilities will cause fluctuations in the measured signal output thus generating correlated effects in the reconstructed maps. In this paper we present an analytical study of the impact of periodic signal fluctuations on the measured sky maps produced by the PLANCK survey. In particular we show how it is possible to estimate analytically the damping factor of the peak-to-peak amplitude of the fluctuation at the instrument output after the projection in the final maps.