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File:Convolution of box signal with itself.gif

Convolution_of_box_signal_with_itself.gif ‎(474 × 145 pixels, file size: 77 KB, MIME type: image/gif, looped, 280 frames, 14 s)

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Summary edit

Description An animation displaying the process and result of convolving a box signal with itself. For each position in the resulting hat function the input functions and the multiplied input functions are shown, and the area which is integrated is marked. This work mimicks [1] but includes the source code and shows the result of the convolution in the same graph as the input functions.
Date
Source Own work
Author Brian Amberg
 
This diagram was created with MATLAB.

Matlab Code used to create this animation edit 

%% Create folding of two rectangular impulses
X=-2.8:0.001:2.8;
F1=zeros(size(X)); F1(abs(X)<=0.5) = 1;
F2=zeros(size(X)); F2(abs(X)<=0.5) = 1;
clf

[tmp zero_offset] = min(abs(X));
!rm -f /tmp/conv_box_box*.png
integral=nan(size(X));
for offset_i=1:numel(X)
  offset=X(offset_i);
  shift=offset_i-zero_offset;
  F2_shifted = circshift(F2, [1 shift]);
  F2_shifted(1:min(shift, numel(X))) = 0;
  F2_shifted(end+shift:end) = 0;
  product = F2_shifted.*F1;
  integral(offset_i) = sum(product)/numel(X)*(X(end)-X(1));
  
  if (mod(offset_i, 20)==0)
    area(X, product, 'facecolor', 'yellow');
    hold on
    plot(X, F1, 'b', X, F2_shifted, 'r', X, integral, 'k', [offset offset], [0 2], 'k:')
    hold off
    axis([-2 2 0 1.1])
    xlabel('t');
    grid on
    legend('Area under f(t)g(t)', 'f(t)', 'g(t)', '(f*g)(t)');
    axis equal
    drawnow
    set(gcf,'PaperPositionMode','auto')
    print('-dpng', '-r72', '-painters', sprintf('/tmp/conv_box_box_%06d.png', offset_i));
  end
end

Image Magicks convert commandline to create the gif: 

convert -delay 5 -loop 0 conv_box_box_*.png conv_box_box.gif

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I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
GNU head 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.
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Date/TimeThumbnailDimensionsUserComment
current18:44, 7 July 2010Thumbnail for version as of 18:44, 7 July 2010474 × 145 (77 KB)Rubybrian (talk | contribs)Cropped the image and compressed it using the commandline <code> convert -layers Optimize -delay 5 -loop 0 conv_box_box_00*.png conv_box_box.gif </code>
18:14, 7 July 2010Thumbnail for version as of 18:14, 7 July 2010587 × 159 (708 KB)Rubybrian (talk | contribs){{Information |Description=An animation displaying the process and result of convolving a box signal with itself. For each position in the resulting hat function the input functions and the multiplied input functions are shown, and the area which is integ

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