In the research of atmospheric remote sensing based on the hyper-spectral infrared radiance, it is an important step to accurately simulate the hyper-spectral infrared radiance. In this paper, the measurement principle of hyper-spectral infrared radiometer is analyzed, and a forward model is established based on ARTS by concerning about the process of interferograms-truncated and discretization. In the forward model, an ideal discretization spectrum was simulated by ARTS firstly, and then the spectrum was transformed into an interference figure through the inverse Fourier transform. After the interference figure was truncated by a specific window function, the Fourier transform was further applied to obtain the simulated spectrum (called “target spectrum” in this paper). During this process, the window function type is dependent on the method of truncation of interference figure in the instrument measurement, (for example, a rectangular function corresponds to an interference figure without a truncation process by apodization function), and both the inverse Fourier transform and the Fourier transform must satisfy the Nyquist sampling law. Based on the forward model, 108 groups of clear sky radiation data in SGP site have been simulated, and the simulation results were compared with the actual measurement results of AERI. The results showed that there was notable difference between ideal spectrum and the spectrum measured by AERI on the gases absorption line, and the maximum residual reached around 35 RU. When a truncation process was added to the simulated spectrum, the maximum residual was constrained within 10 RU, indicating that the truncation process can improve accuracy of the simulated spectrum, especially in the gases absorption lines. Furthermore, the simulated spectrum obtained from six commonly used window function was compared with the spectrum measured by AERI. The results showed that the spectrum processed with rectangular window was most close to AERI measured spectrum, which meant that the window function used in AERI can be seen as a rectangle function. Because the ideal spectral resolution determines the sample rate of the interference figure and computation efficiency of ARTS in transformation of the ideal spectrum to interference figure, it is necessary to find an appropriate ideal spectral resolution to guarantee both the modeling accuracy and efficiency. For this purpose, instrument measurement spectrum were simulated with different ideal spectral resolution, and the residuals between simulated radiations and AERI measured radiations were analyzed. Meanwhile, the influence of spectral resolution on the computational time was discussed. The results showed that when the ideal spectral resolution is set as 0.241 1 cm-1 in the forward mode, the model calculation efficiency can be maximized on the premise of modeling accuracy.