地球重力场有限连续Fourier分析

The Continuous and Finite Fourier Analysis for the Earth's Gravity Field

在Ｆｏｕｒｉｅｒ变换下，从采样函数ｓｉｎｃ（πｘ）与矩形脉冲、ｓｉｎｅ２（πｘ）与山形脉冲的映象关系出发，本文引入采样函数ｓｉｎｃ（πｘ）、ｓｉｎｃ２（πｘ）完成了有限离散Ｆｏｕｒｉｅｒ变换向有限连续Ｆｏｕｒｉｅｒ变换的过渡，在原函数频宽有限的情况下，彻底解决了以往方法造成的混进、泄漏、周期延拓等误差。其次，引入一组变量替换，完成了奇异积分向常规积分的转化。最后模型上的试算展示了本方法的良好应用前景。

Starting from the relationships between a sampling function sine(πx)and a rectangular inupulse function π(x)or a peak impulse funtion △ (x), the procedure from the discrete and finite Fourier transform to the continuous and finite Fourier one is performed in the paper, And then, using a slope variable, the conversion from a singular integral to a non-singular one is carried out, Finally, numerical examples show their feasibility.