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File:Dirac function approximation.gif

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Dirac_function_approximation.gif(200 × 335 pixels, file size: 89 KB, MIME type: image/gif, looped, 10 frames, 2.0 s)
Description

Illustration of approximating the Dirac delta function by gaussians.

Date (UTC)
Source self-made with MATLAB
Author Oleg Alexandrov


Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code (MATLAB)[edit]

% Illustration of approximating the Dirac delta function with gaussians.

function main()

   r = 3; % the power in the Bernoulli inequality
   
   % KSmrq's colors
   red    = [0.867 0.06 0.14];
   blue   = [0, 129, 205]/256;
   green  = [0, 200,  70]/256;
   yellow = [254, 194,   0]/256;
   white = 0.99*[1, 1, 1];

  % Set up the grid and other parameters
   N = 300;
   A = -2; B = 2; 
   C=-1; D = 6;

   X = linspace(A, B, N);
   
   % Set up the figure
   lw = 3; % linewidth
   fs = 18; % font size

   for p=1:10

      a=1/p;

      % gaussian
      Y=(1/(a*sqrt(pi)))*exp(-X.^2/a^2);

      figure(1); clf; 

      set(gca, 'fontsize', fs);
      set(gca, 'linewidth', 0.4*lw)
      hold on;
      
      plot_axes (A, B, C, D, lw/1.5);
      
      plot(X, Y, 'color', blue, 'linewidth', lw);
      
      axis equal; axis([A, B, C, D]); 
      
      set(gca, 'XTick', [-2, -1, 0, 1, 2]) % text labels on the x axis
      grid on;
      
      H=text(B-1.5, D-0.5, sprintf('a=1/%d', p), 'fontsize', fs);

      % save to disk
      file = sprintf('Frame%d.eps', 1000+p);
      disp(file);
      saveas(gcf, file, 'psc2')
      
      pause(0.1);

   end

 % Converted to gif with the command
 % convert -antialias -density 100 -delay 20 -loop 10000 Frame10* Dirac_function_approximation.gif
 % then scaled in Gimp   
   
function plot_axes (A, B, C, D, lw)
   
   gray = 0.5*[1, 1, 1];
   
   plot([A B], [0, 0], 'linewidth', lw, 'color', gray);
   plot([0, 0], [C, D], 'linewidth', lw, 'color', gray);

File history

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Date/TimeThumbnailDimensionsUserComment
current22:51, 12 January 2008Thumbnail for version as of 22:51, 12 January 2008200 × 335 (89 KB)Oleg Alexandrovtweak
22:22, 12 January 2008Thumbnail for version as of 22:22, 12 January 2008217 × 363 (99 KB)Oleg Alexandrov{{Information |Description=Illustration of approximating the Dirac delta function by gaussians. |Source=self-made with MATLAB |Date=~~~~~ |Author= Oleg Alexandrov |Permission= |other_versions= }} {{
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