task1.m

load_data
clf

%% Generate the s[n] signal.
s = zeros(length(T1_data_Sk_BPSK),1);
N = length(s);
for n=1:N
    for k=1:N
        s(n) = s(n) + T1_data_Sk_BPSK(k)*exp(1i*2*pi*n*k/N);
    end
    s(n) = s(n)/sqrt(N);
end

s_r = real(s);
s_i = imag(s);

[p_r, x_r] = hist(s_r);
[p_i, x_i] = hist(s_i);

mu_r = mean(s_r);
mu_i = mean(s_i);
mu_s = mu_r + 1i*mu_i;
E_si_si = mean(s_r.*s_i)

var_r = var(s_r);
var_i = var(s_i);
var_s = var_r + var_i;
sigma_s = sqrt(var_s);

%% Plot pdf(s)

figure(1)
plot(x_r, p_r/sum(p_r));
hold on;
plot(x_i, p_i/sum(p_i));
legend('p(s_r)', 'p(s_i)')

figure(2)
x = -3:.1:3;
y = normpdf(x, real(mu_s), sigma_s);
plot(x, y);
hold on
[p_g, x_g] = hist(T1_data_Sk_Gaussian);
plot(x_g, p_g/sum(p_g));
legend('p(s)', 'p(s_{gaussian})')