Some improvements in practical Fourier analysis and their application to x-ray scattering from liquids
Some improvements in practical Fourier analysis and their application to x-ray scattering from liquids
复制标题
实际傅立叶分析的一些改进及其在液体 X 射线散射中的应用
DOI：
10.1016/s0016-0032(42)90767-1
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发表时间：
1942
影响因子：
4.1
通讯作者：
C. Lanczos
中科院分区：
文献类型：
--
作者：
G. C. Danielson;C. Lanczos
在这些表达式中，u和v的值由方程（7）确定，因此可以直接从原始曲线获得。现在，我们不再通过绘制f~ 2（x）和f~（x）曲线并用求积仪测量面积来产生定积分I~和Is，而是可以通过再次应用方程（66）间接地获得它们，但现在是原始纵坐标数的两倍。由于I1和I2与读数的数量无关，因此将该和与原始和进行比较可以很好地表明我们的近似的有效性。
In these expressions the values for u and v are determined by equation (7) and can, therefore, be obtained directly from the original curve. Now, instead of producing the definite integrals I~ and Is by plotting the f~ 2 (x) and f~(x) curves and measuring the areas by a planimeter, we can obtain them in an indirect way by applying equations (66) again but now to twice the original number of ordinates. Since 11 and I2 are independent of the number of readings, a comparison of this sum to the original sum gives a good indication of the validity of our approximation.