File:Diffractogramme bruit et fourier.png
Diffractogramme_bruit_et_fourier.png (610 × 461 pixels, file size: 6 KB, MIME type: image/png)
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Summary[edit]
Simulation d'un diffractogramme par rayons X du quartz fortement bruité, et sa transformée de Fourier.
La partie gauche du spectre contient le signal ; pour des fréquences supérieures à l'inverse de la largeur des pics, le spectre ne contient que du bruit.
Simulation of the X-ray diffratogram of quartz with a strong noise, and its Fourier transform.
The left part of the spectrum contains the signal; for the frequencies higher than the inverse of the width of the peaks, the spectrum contains only noise.
Auteur/author : Christophe Dang Ngoc Chan (cdang) Réalisé avec/made with Scilab
clear;clf; // domaine : 20 à 50°, pas de 0,02° pas=0.02; // step size freq=1/pas; // sampling frequency x=[20:pas:50]; // 2-theta range // hauteur maximale, largeur et fond continu h=1000; // maximum height s=0.1; // peak width (standard variation) fond=50; // continuous background // Fonction de Gauss function [y]=gauss(x) y=2.5*h/(sqrt(2*%pi))*exp(-x^2/(2*s)) endfunction // pics, désignés par les indices de Miller hkl p100 = 0.16*gauss(x-20.86); p101 = gauss(x-26.64); p110 = 0.09*gauss(x-36.544); p102 = 0.08*gauss(x-39.465); p111 = 0.04*gauss(x-40.3); p200 = 0.06*gauss(x-42.45); p201 = 0.04*gauss(x-45.793); p112 = 0.13*gauss(x-50.139); // diffractogramme d = p100 + p101 + p110 + p102 + p111 + p200 + p201 + p112 + fond; // bruit N = size(d); n=N(1,2); b = rand(1,n,'normal'); b1 = b.*sqrt(d); // Calcul f=d+b1; // diffractogramme ptf = abs(fft(f)); // puissance de la transformée de Fourier for i=1:n if ptf(i)>2e+9 then ptf(i)=2e+9; // saturation end end k=freq*(1:n)/n; // échelle x TF // Affichage subplot(2,1,1) plot2d(x,f,style=2,rect=[20,0,50,h+fond]) xtitle('Simulation du diffractogramme du quartz','2 thêta (°)','intensité (coups)') subplot(2,1,2) plot2d(k,ptf,style=2,rect=[0,100,20,1e5],logflag='nl') xtitle('Transformée de Fourier du diffractogramme','fréq.','Puissance (éch. log.)')
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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current | 16:39, 30 November 2005 | 610 × 461 (6 KB) | Cdang (talk | contribs) | Simulation d'un diffractogramme par rayons X du quartz fortement bruité, et sa transformée de Fourier. ---- Simulation of the X-ray diffratogram of quartz with a strong noise, and its Fourier transform. Auteur/author : Christophe Dang Ngoc Chan ([[us |
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