File:Dirac function approximation.gif
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Dirac_function_approximation.gif (200 × 335 pixels, file size: 89 KB, MIME type: image/gif, looped, 10 frames, 2.0 s)
File information
Structured data
Captions
DescriptionDirac function approximation.gif | Illustration of approximating the Dirac delta function by gaussians. |
Date | (UTC) |
Source | self-made with MATLAB |
Author | Oleg Alexandrov |
Public domainPublic domainfalsefalse |
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
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:51, 12 January 2008 | 200 × 335 (89 KB) | Oleg Alexandrov (talk | contribs) | tweak | |
22:22, 12 January 2008 | 217 × 363 (99 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=Illustration of approximating the Dirac delta function by gaussians. |Source=self-made with MATLAB |Date=~~~~~ |Author= Oleg Alexandrov |Permission= |other_versions= }} {{ |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on ar.wikipedia.org
- Usage on bg.wikipedia.org
- Usage on bn.wikipedia.org
- Usage on cs.wikipedia.org
- Usage on da.wikipedia.org
- Usage on de.wikipedia.org
- Usage on el.wikipedia.org
- Usage on en.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 id.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