Least_square_criterion_plot_against_var.m

clc
close all
%% y (t) = a1 sin(2?f0t) + a2 sin(2?f1t) + n(t), t= 1,....,N
%% plotting J vs variance with fixed fo
f0 = 0.25;
a1 = 1;
a2 = 1;
N = 10000;
t = 1:1:N;
i=1;
var_ = zeros(length(0.1:0.1:1),1);
J1 = zeros(length(0.1:0.1:1),1);
for s_d = 0.1:0.1:1
    n1 = s_d .* n; 
    y = (a1.*sin(2*pi*f0.*t)) + (a2.*sin(2*pi*f1.*t)) + n1;
    var_(i) = var(y);
    y = y';
    J = (y - (a1.*sin(2*pi*f0.*t')) - (a2.*sin(2*pi*f1.*t'))).^2;
    J1(i) = sum(J);
    i = i + 1;
end
plot(var_,J1)
title('Plot of J vs variance with fo and f1constant and a1 = a2 = 1')
ylabel('Amplitude of J')
xlabel('Value of variance')