On the Tore Supra tokamak, a Far Infrared (FIR) polarimeter diagnostic has been routinely used for diagnosing the current density by measuring the Faraday rotation angle. A high precision of measurement is needed to correctly reconstruct the current profile. To reach this precision, electronics used to compute the phase and the amplitude of the detected signals must have a good resilience of the noise present in the measurement chain. In this article, we analyse the way the analogue cards response to the noise coming from the detectors and their impact on the Faraday angle measurements, and we present numerical methods to calculate the phase and the amplitude. These validations have been done by using real signals acquired by Tore Supra and JET experiments. These methods have been developed to be used in real-time in the future numerical cards that will replace the Tore Supra present analogue ones.