L = 2;                              % length
M = 200;                            % number of samples
dx = L/M;                           % sample interval

x = -L/2:dx:L/2-dx;             % x coordinates
f_1 = exp(-pi*(x.^2));          % Gaussian 1
f_2 = exp(-pi*(x.^2));          % Gaussian 2 (same as 1)

figure(1)
plot(x,f_1,x,f_2,'--'); title('functions');
xlabel('x (m)');

%% Step 2. Perform convolution
F_1 = fft(f_1);                     % transform f_1
F_2 = fft(f_2);                     % transform f_2
F_0 = F_1.*F_2;                     % multiply pointwise
f_0 = ifft(F_0)*dx;                 % inverse transform and scale
f = fftshift(f_0);                  % center result

figure(1)
hold on
plot(x,f); title('Convolution');
xlabel('x')