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We report on a theoretical study of polarization impairments in periodically spun fiber Raman amplifiers. Based on the Stochastic Generator approach we have derived averaged equations to calculate polarization dependent gain and mean-square gain fluctuations. We show that periodically spun fiber can work as a Raman polarizer but it suffers from increased polarization dependent gain and gain fluctuations. Unlike this, application of a depolarizer can result in suppression of polarization dependent gain and gain fluctuations. We demonstrate that it is possible to design a new fiber Raman polarizer by combining a short fiber without spin and properly chosen parameters and a long periodically spun fiber. This polarizer provides almost the same polarization pulling for all input signal states of polarization and so has very small polarization dependent gain.