Just choose any arbitrary vector for ‘z’ that is long enough to completely support the signals to be convolved. For a Gaussian, that is relatively easy to describe. (For other signals, it may be less obvious.)
c1 = 1;
s1 = 1;
c2 = 1;
s2 = 1;
% z = %%????
z = (min(c1,c2)-10):(max(c1,c2)+10);
x = exp(-(z-c1).^2/(2*s1.^2));
h = exp(-(z-c2).^2/(2*s2.^2));
y = my_convolution(x, h);
same_range = (fix(numel(y)/2)-fix(numel(z)/2))+(1:numel(z)); % Create 'same' Vector
ys = y(same_range); % Part Of 'y' To Plot
figure;
plot(z,ys)
comp = conv(x, h, 'same');
figure;
plot(z,comp)
function y = my_convolution(x, h)
M = length(x);
N = length(h);
X = [x, zeros(1, N)];
H = [h, zeros(1, M)];
for i = 1 : M + N -1
y(i) = 0;
for j = 1:M
if (j < i + 1)
y(i) = y(i) + X(j)*H(i - j + 1);
else
end
end
end
end
The ‘same_range’ index vector appears to work reasonably well.
Experiment to get different results.
.
