The application of interferometric spectroscopy in many fields, such as atmospheric remote sensing, astronomical exploration and geophysical prospecting, is a research hotspot at home and abroad. Spectral reconstruction, as an important part of remote sensing data processing, is closely related to the detection accuracy. Interferogram due to limited optical path difference sampling results in frequency leakage in the restored spectrum. The apodization function can play a role in smoothing the spectrum, maintaining the spectral consistency of the interferometric spectroscopy and other spectroscopy techniques, but at the same time, the resolution (Full Width at Half Maximum, FWHM) of the reconstructed spectrum will be reduced. It has been shown that the apodization function does not improve the inversion accuracy, and the apodization function is not used in the ground data processing of several typical atmospheric remote sensing loads. Spatial heterodyne spectroscopy (SHS) has attracted wide attention at home and abroad due to its many advantages. Based on this technology, Anhui Institute of Optics and Fine Mechanics of Chinese Academy of Sciences has successfully developed a prototype for atmospheric CO2 detection. Signal-to-noise ratio (SNR) is one of the key indicators of spectrometer. This paper studies the influence of apodization function on spectral reconstruction of interferogram from the relationship between SNR, spectral resolution and detection accuracy. In view of the fact that the traditional apodization function does not achieve the optimal side-lobe suppression, this paper constructs ten apodization functions with different spectral extending based on Norton-Beer apodization function and the criterion of obtaining the maximum side-lobe suppression under the same resolution reduction. Radiative transfer Model of SCIATRAN was used to analyze the difference of atmospheric top radiance caused by different gas concentration in atmospheric CO2 remote sensing. The spectral SNR requirement of different spectral resolution meets the requirement of 1% detection accuracy under typical conditions was calculated. Based on the parameters of the laboratory prototype, the relationship between spectral resolution and SNR under different extending was analyzed by simulating interferogram and constructed apodization function in this paper. Finally, the experimental verification was carried out by using a prototype developed by the laboratory. The interferograms were obtained by observing the stable uniform integrating sphere, and the SNR was calculated without apodization, and the SNR was calculated after different apodization extending. The simulation and experimental results show that of the SNR is gradually increased due to the reduction of noise by apodization, and the spectral resolution is gradually reduced, while the requirement of SNR for detection accuracy is gradually increased due to the decrease of resolution. The spectral SNR requirement of detection accuracy is obviously higher than that under the apodization. The SNR of simulation data and measured data is lower than that of the requirement of detection accuracy when apodization extendings are greater than 1.6 times and 1.8 times, respectively. The need for the SNR of the instrument, that is, the white noise is dominant, is not conducive to the detection accuracy. The results of this paper can be used as a reference for spectral reconstruction, and the influence of inversion accuracy will be further analyzed in the future.