This paper present a new algorithm for the computation of Fourier extension based on boundary data, which can obtain a super-algebraic convergent Fourier approximation for non-periodic functions. The algorithm calculates the extension part through boundary data and connects it with the original function to form a periodic smooth function. By testing the key parameters involved, their impact on the algorithm is clarified and the optimization setting scheme of the parameters is proposed. Compared with FFT, the algorithm only needs to increase the computational complexity by a fixed small amount.

翻译：本文提出了一种基于边界数据计算傅里叶延拓的新算法，该算法可为非周期函数获得超代数收敛的傅里叶近似。算法通过边界数据计算延拓部分，并将其与原函数连接以构成周期光滑函数。通过测试所涉及的关键参数，阐明了其对算法的影响，并提出了参数的优化设置方案。与快速傅里叶变换（FFT）相比，该算法仅需增加固定且少量的计算复杂度。