clear
DADOS = load( 'dados_osciloscopio.txt' );
t = DADOS(:,1);
y = DADOS(:,2);
s = 0.06;
si = s*ones(size(y));
f = 2;

g1 = cos(2*pi*f*t);
g2 = sin(2*pi*f*t);

D(1,1) = (1/s^2)*sum( (y.*g1) );
D(2,1) = (1/s^2)*sum( (y.*g2) );

M(1,1) = (1/s^2)*sum( (g1.*g1) );
M(2,1) = (1/s^2)*sum( (g2.*g1) );
M(1,2) = (1/s^2)*sum( (g1.*g2) );
M(2,2) = (1/s^2)*sum( (g2.*g2) );

VA = inv( M );
A = VA * D;
Gtil = A(1)*g1 + A(2)*g2;

a1 = A(1)
s_a1 = sqrt( VA(1,1) )
a2 = A(2)
s_a2 = sqrt( VA(2,2) )
cov_a1a2 = VA(1,2)
rho_a1a2 = cov_a1a2 / ( s_a1 * s_a2 )

R = y - Gtil;
figure
subplot(3,1,1:2)
plot( t, y, '*')
hold on
plot( t, Gtil, '-r', 'linewidth', 3 )

subplot(3,1,3)
plot( t, R, '*')
hold on
plot( t, zeros(size(R)), '-r', 'linewidth', 3 )