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.
% Create folding of two rectangular impulsesclearX=-2.6:0.001:3;F1=abs(X)<=1.5;F2=abs(X)<=1.5;clfmkdir('tmp');[tmpzero_offset]=min(abs(X));SyncFrames=[1round(18.67*(1:numel(X)))];integral=nan(size(X));frame=1;foroffset_i=1:numel(X);offset=X(offset_i);shift=offset_i-zero_offset;F2_shifted=circshift(F2,[0shift]);product=F2_shifted.*F1;integral(offset_i)=sum(product)/numel(X)*(X(end)-X(1));ifoffset_i==SyncFrames(frame)frame=frame+1;area(X,product,'facecolor','yellow');holdonplot(X,F1,'b',X,F2_shifted,'r',X,integral,'k',[offsetoffset],[02],'k:')holdoffaxisimageaxis([-2.12.101.1])xlabel('\tau & t');gridonlegend('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));drawnowendendsystem('"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:
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
{{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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