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A study on interpolation and weighting function for numerical Fourier transform

机译：数字傅里叶变换的插值和加权功能研究

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In order to mitigate the Gibbs oscillation, a very simple and effective linear mid-point interpolation method is proposed. The relationship between proposed linear mid-point interpolation in time domain and window function in numerical inverse Fourier transform is also investigated in this paper. It is proved that the linear mid( ) point interpolation in time domain is equivalent to the cosine window function defined as Gcos(?) = cos? ? , 2 ?max where ?max is the maximum angular frequency used in the transform. Furthermore, the cosine window function and sinc window function (also known as sigma-factor) show the similar characteristic. A weighting order n, which is originally defined as the power to which the window function is raised, can also be applied to the interpolation method when n is an integer. The nth-time interpolation is equivalent to applying the window function [Gcos(?) ]n in frequency domain.
机译：为了缓解GIBBS振荡，提出了一种非常简单有效的线性中点插值方法。 本文还研究了在数值逆傅立叶变换中的时域和窗口功能之间提出的线性中点插值之间的关系。 事实证明，时间域中的线性MID（）点插值等同于余弦窗口函数定义为GCOS（？）= COS？ 还是 ，2？最大值在哪里？最大值是变换中使用的最大角度频率。 此外，余弦窗口功能和SINC窗口功能（也称为SIGMA系数）显示了类似的特性。 当n是整数时，还可以将最初定义为窗口函数升高为窗口功能的电源的加权顺序n。 nth-time插值等同于在频域中应用窗口函数[GCOS（α）] n。

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