# Hypothesis Test on Gaussian Mixture

I have data blocks being received at a node which can be presumed to be Gaussian sequence, $X(m_1,sigma_1).$ In some of the blocks a separate Gaussian stream $Y(m_2,sigma_2)$ adds to the original stream and intended receiver gets a mixture.

1. I am interested in figuring out if the block I am receiving is with or without external mix.

The issue is $m_1$ and $sigma_1$ and $m_2$ and $sigma_2$ are not known a priori. Can Gaussian Mixture Classifier help?

This isn't really a case of a mixture, but of a random effect. One of the signals will be the "pure" gaussian sequence: $X(m_1,\sigma_1)$, the second will be the gaussian signal: $X(m_1+m_2,\sqrt{\sigma_1+\sigma_2})$.
• Replace $\sqrt{\sigma_1+\sigma_2}$ by $\sqrt{\sigma_1^2+\sigma_2^2}$. – Did Feb 26 '15 at 10:56