# File:Dirac function approximation.gif

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 12 January 2008, 22:22 (UTC) Source self-made with MATLAB Author Oleg Alexandrov

 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)

```% 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

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current22:51, 12 January 2008200 × 335 (89 KB)Oleg Alexandrovtweak
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= }} {{
The following pages on the English Wikipedia link to this file (pages on other projects are not listed):

## Global file usage

The following other wikis use this file:

• Usage on ar.wikipedia.org
• Usage on cs.wikipedia.org
• Usage on de.wikipedia.org
• Usage on el.wikipedia.org
• Usage on en.wikibooks.org
• Usage on fa.wikipedia.org
• Usage on fi.wikipedia.org
• Usage on fr.wikipedia.org
• Usage on he.wikipedia.org
• Usage on hi.wikipedia.org
• Usage on hu.wikipedia.org
• Usage on it.wikipedia.org
• Usage on ka.wikipedia.org
• Usage on ko.wikipedia.org
• Usage on nl.wikipedia.org
• Usage on no.wikipedia.org
• Usage on pt.wikipedia.org
• Usage on ro.wikipedia.org
• Usage on simple.wikipedia.org
• Usage on si.wikipedia.org
• Usage on sl.wikipedia.org
• Usage on sr.wikipedia.org
• Usage on sv.wikipedia.org
• Usage on uk.wikipedia.org
• Usage on vi.wikipedia.org
• Usage on zh.wikipedia.org