deletions | additions       diff --git a/Waveform optimization.tex b/Waveform optimization.tex  index a1f6976..0525a30 100644  --- a/Waveform optimization.tex  +++ b/Waveform optimization.tex 
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The joint distribution of hidden states $P(X|D,\Theta)$ is given by $\prod_i^N P(x_1^i,..,x_{T_i}^i|d_1^i,..,d_{T_i}^i,\Theta)$.  substituting Substituting  into Eq.\ref{eqn:Qem} we find: \begin{equation}   \int_X \sum_{i=1}^N [ \sum_{t=1}^{T_i} (d_t^i - m(x_t^i))^2 ]P(X|D,\Theta_{k-1}) + \int_X \sum_{i=1}^N [ \log(P(X|\Theta_{k}))]P(X|D,\Theta_{k-1})