Example MATLAB Code to create visualization of Convolution

% Create folding of two rectangular impulses

clear

clc

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');