In the Fourier transform infrared spectrometers, the interferograms are usually sampled by means of the single-side beyond zero path difference and the interferograms are asymmetric. In order to realize the Fourier cosine transform and truly rebuild the spectrum, the phase-corrected technologies of Forman is researched and improved. In the Forman method, the convolution is used in several times so that the operation is complication and it is difficult to realize by the hardware circuits. The linear convolution is realized though three fast fourier transform (FFT) operation to reduce the quantity of computation. It is found that quantity of the short double-side data, apodization function and the times of phase correction affect the result of the corrected interferograms in the experiment. The 500 K infrared blackbody is used as the radiant source to achieve the absorption spectrum of the atmosphere in the infrared range. The single-side beyond zero interferograms is achieved by the HgCdTe dot diode detection. The interferograms are corrected and rebuilded by the improved Forman method. The spectral resolution of the rebuild absorption spectrum is 4 cm-1 and the wavenumber error is little. which show the higher accuracy of spectrometers.