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)

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 mimics [1] but includes the source code and shows the result of the convolution in the same graph as the input functions.
Date	2010-07-25 23:41 (UTC)
Source	Convolution_of_box_signal_with_itself.gif
Author	Convolution_of_box_signal_with_itself.gif: Brian Amberg derivative work: Tinos (talk)

This chart was created with MATLAB.

MATLAB Code

% Create folding of two rectangular impulses
 
clear
 
X=-2.6:0.001:3;
F1=abs(X)<=0.5;
F2=abs(X)<=0.5;
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

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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File history

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	Date/Time	Thumbnail	Dimensions	User	Comment
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