File:Convolution of box signal with itself.gif

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

Summary

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	7/7/2010
Source	Own work
Author	Brian Amberg

This chart was created with MATLAB.

Matlab Code used to create this animation

%% 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

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses: You may select the license of your choice.

File history

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	18:44, 7 July 2010		474 × 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 2010		587 × 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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• Usage on en.wikipedia.org
  • Talk:Pulse compression