Convolution of two Gaussian functions without conv

I am attempting to perform the convolution of two Gaussian functions, x and h, without using conv and then comparing that with the convolution solved by the built-in conv. I'm stuck setting the parameter for z and the x-axis for the two plots. Below is what I have come up with. Any help would be appreciated!

c1 = 1;
s1 = 1;
c2 = 1;
s2 = 1;

z = %%????
x = exp(-(z-c1).^2/(2*s1.^2));
h = exp(-(z-c2).^2/(2*s2.^2));

y = my_convolution(x, h); 
figure;
plot(???,y)

comp = conv(x, h, 'same');
figure;
plot(???,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

Answer 1

[Star Strider]

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.

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