No higher resolution available.
Convolution_of_box_signal_with_itself.gif (474 × 145 pixels, file size: 77 KB, MIME type: image/gif, looped, 280 frames, 14 s)
 | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
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 | |
| Source | Own work |
| Author | Brian Amberg |
![[1]](https://en.wikipedia.org/wiki/File:Convolucion_Funcion_Pi.gif){kind=link}
This diagram 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:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- 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.
|
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. |
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 18:44, 7 July 2010 | | 474 × 145 (77 KB) | Rubybrian | 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 | {{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 |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
