File:Convolution of box signal with itself2.gif
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Convolution_of_box_signal_with_itself2.gif (468 × 147 pixels, file size: 83 KB, MIME type: image/gif, looped, 301 frames, 15 s)
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DescriptionConvolution of box signal with itself2.gif | 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 mimics [1] but includes the source code and shows the result of the convolution in the same graph as the input functions. |
Date | (UTC) |
Source | |
Author |
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This diagram was created with MATLAB.
MATLAB Code
[edit]% Create folding of two rectangular impulses
clear
X=-2.6:0.001:3;
F1=abs(X)<=1.5;
F2=abs(X)<=1.5;
clf
mkdir('tmp');
[tmp zero_offset] = min(abs(X));
SyncFrames=[1 round(18.67*(1:numel(X)))];
integral=nan(size(X));
frame=1;
for offset_i=1:numel(X);
offset=X(offset_i);
shift=offset_i-zero_offset;
F2_shifted = circshift(F2, [0 shift]);
product = F2_shifted.*F1;
integral(offset_i) = sum(product)/numel(X)*(X(end)-X(1));
if offset_i==SyncFrames(frame)
frame=frame+1;
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 image
axis([-2.1 2.1 0 1.1])
xlabel('\tau & t');
grid on
legend('Area under f(\tau)g(t-\tau)', 'f(\tau)', 'g(t-\tau)', '(f\astg)(t)');
print('-dpng','-r72',sprintf('tmp/conv_box_box_%06d.png', offset_i));
drawnow
end
end
system('"C:\Program Files\ImageMagick-6.6.3-Q16\convert.exe" -layers Optimize -delay 5 tmp/conv_box_box_*.png conv_box_box.gif');
delete('tmp/*');
rmdir('tmp');
Photoshop was then used to crop the animation.
This is a retouched picture, which means that it has been digitally altered from its original version. Modifications: Fixed asterisk, and put tau in.. The original can be viewed here: Convolution of box signal with itself.gif: . Modifications made by Tinos.
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Original upload log
[edit]This image is a derivative work of the following images:
- File:Convolution_of_box_signal_with_itself.gif licensed with Cc-by-sa-3.0, GFDL
- 2010-07-07T18:44:30Z Rubybrian 474x145 (79321 Bytes) Cropped the image and compressed it using the commandline convert -layers Optimize -delay 5 -loop 0 conv_box_box_00*.png conv_box_box.gif
- 2010-07-07T18:14:59Z Rubybrian 587x159 (725000 Bytes) {{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 show
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 10:11, 26 July 2010 | 468 × 147 (83 KB) | Tinos (talk | contribs) | Synchronised with Convolution_of_spiky_function_with_box2.gif. | |
23:47, 25 July 2010 | 470 × 150 (78 KB) | Tinos (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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Software used | Adobe Photoshop CS5 Windows |
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