The Vostok ice core provides measurements of the CO₂ concentration during the last 414 × 10³ years (yr). Estimations of power spectra show peaks, with the strongest one corresponding to a time period of around 100 × 10³ yr. In this paper, a new reconstruction method from irregular sampling is used, allowing more accurate estimation of spectral peaks. This method intrinsically decomposes the analyzed signal as a sum of sines, providing amplitudes but also phase measurements of periodic tendencies (due to the nature of the studied phenomena). This decomposition can be conducted with noisy and inaccurate measurements of the sampling instants and the concentrations. The widely used Vostok data were chosen as an example, but the method could also be applied to data from other places (e.g., dome C, Antarctica) or to study other phenomena as nitrogen dioxide NO₂, methane CH₄, oxygen isotope ¹⁸O (closely linked to temperature), deuterium ²H, or dust concentrations.