Finding the likeliest observations and state sequence

This gives us the likeliest observation sequence for a given state sequence. The state sequence is partly determined by the synthesis specification in that we know the words and phones, but not the state sequence within each phone. Ideally, we would search every possible state sequence to find the observation sequence that maximise c in Equation (15.31), but this is too expensive, firstly because the munber of possible state sequences is very large and secondly because the solution of Eqnation (15.31) for each possible state sequence is expensive. 

This result shows us how to generate from HMMs while also obeying the dynamic constraints of the delta coefficients. In further papers, Tokuda, his colleagues and others have extended this basic result to include any number of delta coefficients (e.g. acceleration coefficients, third-order deltas and so on) [453], exphcit duration modelling [514], use ofmore-sophisticated trajectory modelling [133], [134], [454], [513], use of multiple Gaussian mixtures and use of streams, which will be explained below. 

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