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File:Convolution of spiky function with box.gif

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Convolution_of_spiky_function_with_box.gif (475 × 144 pixels, file size: 106 KB, MIME type: image/gif, looped, 406 frames, 20 s)

Summary

Description

An animation displaying the process and result of convolving a spiky 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 File:Convolucion de entrada con respuesta al impulso.gif but includes the source code and shows the result of the convolution in the same graph as the input functions.

The function used is $exp(-t)$ for $t>0$ and $0$ otherwise.
Date
Source Own work
Author Brian Amberg
 
This diagram was created with MATLAB.


Matlab Code used to create the image

%% Create folding of two rectangular impulses with spiky function
X=-2.3:0.0005:3.8;
F1=exp(-X);
F1(X<=0) = 0;
F2=zeros(size(X)); F2(abs(X)<=0.5) = 1;
clf

[tmp zero_offset] = min(abs(X));

!rm -f /tmp/conv_box_spike*
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, 30)==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([-1.5 3 0 1.1])
    xlabel('t');
    legend('Area under f(t)g(t)', 'f(t)', 'g(t)', '(f*g)(t)');
    grid on
    drawnow
    
    set(gcf,'PaperPositionMode','auto')
    print('-dpng', '-r72', '-painters', sprintf('/tmp/conv_box_spike_%06d.png', offset_i));
    
  end
end

And the conversion was done with Image Magicks convert using convert -delay 5 -loop 0 conv_box_spike_*.png conv_box_spike.gif

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
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  • 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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7 July 2010

image/gif

57b815311893d245922d992af97e71a1541375ff

108,640 byte

20.300000000000153 second

144 pixel

475 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current18:41, 7 July 2010Thumbnail for version as of 18:41, 7 July 2010475 × 144 (106 KB)RubybrianCropped the image and optimized the output for size using <code> convert -layers Optimize -delay 5 -loop 0 conv_box_spike_*.png conv_box_spike.gif </code>
18:22, 7 July 2010Thumbnail for version as of 18:22, 7 July 2010587 × 159 (1.03 MB)Rubybrian== Summary == {{Information |Description=An animation displaying the process and result of convolving a spiky signal with itself. For each position in the resulting hat function the input functions and the multiplied input functions are shown, and the are

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