File:Convolution of spiky function with box.gif
Summary
| 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 functions are shown, and the area which is integrated is marked. This work mimicks 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 $exp(-t)$ for $t>0$ and $0$ otherwise. |
| Date | |
| Source | Own work |
| Author | Brian Amberg |
This diagram was created with MATLAB.Category:PNG created with MATLAB#Convolution%20of%20spiky%20function%20with%20box.gif
Matlab Code used to create the image
%% Create folding of two rectangular impulses with spiky function
X=-2.3:0.0005:3.8;
F1=exp(-X);
F1(X<=0) = 0;
F2=zeros(size(X)); F2(abs(X)<=0.5) = 1;
clf
[tmp zero_offset] = min(abs(X));
!rm -f /tmp/conv_box_spike*
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, 30)==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([-1.5 3 0 1.1])
xlabel('t');
legend('Area under f(t)g(t)', 'f(t)', 'g(t)', '(f*g)(t)');
grid on
drawnow
set(gcf,'PaperPositionMode','auto')
print('-dpng', '-r72', '-painters', sprintf('/tmp/conv_box_spike_%06d.png', offset_i));
end
end
And the conversion was done with Image Magicks convert using
convert -delay 5 -loop 0 conv_box_spike_*.png conv_box_spike.gif
Licensing
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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. |
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