File:Convolution of spiky function with box2.gif

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Convolution_of_spiky_function_with_box2.gif (468 × 135 pixels, file size: 76 KB, MIME type: image/gif, looped, 301 frames, 15 s)

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Captions

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Description An animation displaying the process and result of convolving a box signal with a spiky impulse response. 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 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 for and 0 otherwise.
Date (UTC)
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This diagram was created with MATLAB.

MATLAB Code

[edit]
% Create folding of rectangular impulse with spiky function

clear

X=-2.1:0.001:4;
F1=exp(-X);
F1(X<0)=0;
F2=abs(X)<=0.5;
clf

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

SyncFrames=[1 round(20.3366666*(1:numel(X)))];
frame=1;
integral=nan(size(X));
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([-1.6 3.1 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_spike_%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_spike_*.png conv_box_spike.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 spiky function with box.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_spiky_function_with_box.gif licensed with Cc-by-sa-3.0, GFDL
    • 2010-07-07T18:41:06Z Rubybrian 475x144 (108640 Bytes) Cropped the image and optimized the output for size using convert -layers Optimize -delay 5 -loop 0 conv_box_spike_*.png conv_box_spike.gif
    • 2010-07-07T18:22:54Z Rubybrian 587x159 (1081595 Bytes) == 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 fu

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Date/TimeThumbnailDimensionsUserComment
current10:12, 26 July 2010Thumbnail for version as of 10:12, 26 July 2010468 × 135 (76 KB)Tinos (talk | contribs)Synchronised with Convolution_of_spiky_function_with_box2.gif.
00:20, 26 July 2010Thumbnail for version as of 00:20, 26 July 2010469 × 143 (57 KB)Tinos (talk | contribs){{Information |Description=An animation displaying the process and result of convolving a box signal with a spiky impulse response. For each position in the resulting hat function the input functions and the multiplied input functions are shown, and the a

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