Diffraction Methods in Structure Analysis

Abstract

Any continuous differentiable function Ѱ(x) may be expanded by its Fourier series:

$$ \begin{array}{*{20}{c}} {\psi \left( x \right) = {A_0} + 2\sum\limits_{n = 1}^\infty {\left[ {{A_n}\cos 2\pi n\left( {x/a} \right) + {B_n}\sin 2\pi n\left( {x/a} \right)} \right]} } \\ { = \sum\limits_{ - \infty }^\infty {\left[ {{A_n}\cos 2\pi n\left( {x/a} \right) + {B_n}\sin 2\pi n\left( {x/a} \right)} \right]} } \end{array} $$

((4.1))

where a is the period, A₀, A _n and B _n are constants, and A _n = A _n and B _n = −B_−n. This means that for each given x, the value of Ѱ (x) may be obtained by adding the sine and the cosine harmonics, if the appropriate coefficients A_n and B _n are selected for each harmonic.