逆傅里叶积分变换与沿实轴无穷区间主值积分公式

Inverse Fourier integral transform and integral formulas with infinite interval principal value along the real axis

傅里叶积分变换是工程技术和科学研究不可缺少的分析工具,但其逆变换计算比较困难。研究发现,逆傅里叶积分变换是实自变量复函数沿复平面实轴无穷区间上的主值积分,可转化为复变函数的环路积分,并利用留数计算来完成,我们导出的实自变量复函数沿复平面实轴无穷区间上的主值积分公式,可用于逆傅里叶积分变换的快速计算。

Fourier integral transform is an indispensable analysis tool in the engineering technology and scientific research, but inverse Fourier integral transform computation is very difficult. Research has found that the inverse Fourier integral transform can be transformed into closed path integral of the complex functions, using the residue theorem to complete calculation. The principal value integral formulas derived, can be used for inverse Fourier integral transform fast calculation.