The sampling mode of static Fourier transform spectrometer is spatial domain sampling. The interferogram function is sampled by two orthogonal stepped mirrors and the interference irradiance is received by the detector. The interferogram image is a planar spatial array which consists of M×M interferogram units. After image segmentation, the interferogram image is divided into M×M interferogram units according to comparability criterion. By means of addressing location, the sampled interferogram sequence which matches up to the discrete optical path difference sequence could be gained. Using over-zero sampling technique, the big single side interferogram sequence and the small double side interferogram sequence are apodizated by different window functions. For the sake of correcting phase error, the frequency-domain spectrum correction and space-domain interferogram correction are researched and improved. The simulation result shows that the two methods can both gain the perfect spectrum line shape, and the effect of space-domain interferogram correction is better than others with the spectrum standard deviation only 0.012 088.