Correct determination of the phase spectrum is a highly relevant task in Fourier transform spectrometry for concluding which spectral distribution most likely gave rise to the measured interferogram. We present implementation of an improved scheme for phase determination in the operational Collaborative Carbon Column Observing Network (COCCON) processor. We introduce a robust unwrapping scheme for retrieving a spectrally smooth phase spectrum at intermediate spectral resolution, which uses all spectral positions carrying enough signal to allow a significant determination of the phase. In the second step, we perform a least-squares fit of model parameters of a suitable analytical phase spectrum model through all reliable phase values constructed in the first step. The model fit exploits the fact that we expect the phase to be spectrally smooth. Still, it can be refined to reflect specific characteristics inherent to the optical and electronic layout of the interferometer. The proposed approach avoids the problems of the classical phase reconstruction method, which enforces a spectrally smooth phase by directly limiting spectral resolution when calculating the complex phase. Thereby, the phase is created from a very low number of interferogram points around the centerburst of the interferogram, which results in a suboptimal noise propagation from the interferogram into the spectral domain. Moreover, the interpolation of the phase spectrum across spectral subsections with reduced spectral signal is not well behaved, and results depend strongly on the numerical apodization function used for creating the low-resolution phase.