function psi = gaussian_modulated_cosine(t, f, sigma)
    % gaussian_modulated_sine: 
    % input:
    %   t - time grid
    %   f -  frequency of the sinusoid
    %   sigma - standard deviation of the gaussian
    %
    % output:
    %   psi - sinusoid modulated by a Gaussian
        % normalization factor
    c = 1 / (sigma * sqrt(2*pi));
    psi = c * exp(-t.^2 / (2 * sigma^2)) .* cos(2 * pi * f * t);
end