Abstract: In a Fourier spectrometer arrangement for Fourier transforming an interferogram for determining the optic spectrum of a radiation, the readout of the interferogram is decoupled from particular phase positions of the reference signal through elimination of otherwise required synchronization with an external fixed clock pulse to thereby enable a lowering of the reference frequency and simultaneously to maintain or increase the scan frequency of the interferogram. The Fourier spectrometer arrangement includes an extrapolation filter which receives the incoming reference signal and employs adaptive state estimation processes in order to generate extrapolation values by which the future course of the reference signal can be projected. These extrapolation values can be calculated at times which are closer together than, e.g., zero crossings of the reference signal and may have an arbitrary phase position thereto.