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Diffractogramme bruit et fourier.png

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Diffractogramme_bruit_et_fourier.png(610 × 461 pixels, file size: 4 KB, MIME type: image/png)

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.)')

Licensing Edit

Heckert GNU white 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."
This page uses content from the Wikimedia Commons. The original content was at File:Diffractogramme bruit et fourier.png. The list of authors can be seen in the page history. As with this Psychology Wiki wiki, that portion of the content of Wikimedia Commons is available under the GNU Free Documentation License.

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Date/TimeThumbnailDimensionsUserComment
current11:29, November 5, 2007Thumbnail for version as of 11:29, November 5, 2007610 × 461 (4 KB)PhloxBot (Talk | contribs)== Summary == 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

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