Accurate synthetic spectra that rely on large Line-By-Line (LBL)-databases are used in a wide range of applications such as high temperature combustion, atmospheric re-entry, planetary surveillance and laboratory plasmas. Conventionally synthetic spectra are calculated by computing a lineshape for every spectral line in the database and adding those together, which may take multiple hours for large databases. In this paper we propose a new approach for spectral synthesis based on an integral transform: the synthetic spectrum is calculated as the integral over the product of a Voigt profile and a newly proposed three-dimensional “lineshape distribution function”, which is a function of spectral position and Gaussian- & Lorentzian width coordinates. A fast discrete version of this transform based on the Fast Fourier Transform (FFT) is proposed, which improves performance compared to the conventional approach by several orders of magnitude while maintaining accuracy. Strategies that minimize the discretization error are discussed. A Python implementation of the method is compared against state-of-the-art spectral code RADIS, and is since adopted as RADIS's default synthesis method. The synthesis of a benchmark CO₂ spectrum consisting of 1.8 M spectral lines and 200k spectral points took only 3.1 s using the proposed method (10¹¹ lines × spectral points/s), a factor $\sim$300 improvement over the state-of-the-art, with the relative improvement generally increasing for higher number of lines and/or number of spectral points. An experimental GPU-implementation of the method was also benchmarked, which demonstrated another 2~3 orders performance increase, achieving up to 5 ⋅ 10¹⁴ lines × spectral points/s.

依靠大型逐行（LBL）数据库的精确合成光谱可用于多种应用，例如高温燃烧，大气重入，行星监测和实验室等离子。常规上，合成光谱是通过计算数据库中每条光谱线的线形并将它们相加来计算的，大型数据库可能要花费多个小时。在本文中，我们提出了一种基于积分变换的光谱合成新方法：将合成光谱计算为Voigt轮廓与新提出的三维“线形分布函数”乘积的积分”，它是光谱位置以及高斯和洛伦兹宽度坐标的函数。提出了基于快速傅立叶变换（FFT）的此变换的快速离散版本，与传统方法相比，该方法将性能提高了几个数量级，同时保持了准确性。讨论了最小化离散化误差的策略。该方法的Python实现与最先进的频谱代码RADIS进行了比较，并被采用为RADIS的默认综合方法。使用所提出的方法（10 ¹¹线×光谱点/ s），由1.8 M光谱线和200k光谱点组成的基准CO ₂光谱的合成仅需3.1 s$〜$相对于现有技术有300的改进，相对的改进通常随着线数和/或光谱点数量的增加而增加。还对该方法的实验性GPU实现进行了基准测试，该方法证明了性能又提高了2〜3阶，达到了5⋅10 ¹⁴线×光谱点/秒。