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Improved method for the discrete fast Fourier transform

机译：离散快速傅立叶变换的改进方法

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A new algorithm is proposed here for the discrete fast Fourier transform with greatly reduced aliasing which is known to be inherent in the conventional algorithm of Cooley and Tukey, unless the function is band limited and the sampling frequency satisfies the Nyquist condition. Like the algorithm recently proposed by Schütte and extended by Mäkinen in this journal, this is also based on the polynomial expansion of the function to be transformed but more general in formulation and less restrictive than theirs. Its power is demonstrated with a few non‐band‐limited functions that can be exactly transformed with chosen limits as usually met in different experimental situations. In all cases tried, this yields, in general, much improved accuracy in comparison to others at little or no corresponding increase of computation time.
机译：这里提出了一种新的算法，用于离散快速傅里叶变换，具有大大减少的混叠，这是Cooley和Tukey的常规算法中固有的，除非该函数受频带限制且采样频率满足Nyquist条件。就像Schütte最近提出并由Mäkinen在该期刊中扩展的算法一样，这也基于要转换的函数的多项式展开，但其表达形式更为笼统，并且约束性较小。它的功能通过一些非频带限制的功能得到了证明，这些功能可以根据通常在不同实验情况下遇到的选定限制进行精确转换。在所有尝试的情况下，总的来说，与之相比，在几乎不增加计算时间或根本不增加计算时间的情况下，其准确性大大提高。

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