At synthesis time we have a stream of target segments that we wish to synthesize. For each target we use the CART for that unit type, and ask the questions to find the appropriate cluster which provides a set of candidate units. The function Tdist(U) is defined as the distance of a unit U to its cluster center, and the function as the join cost of the optimal coupling point between a candidate unit and the previous candidate unit it is to be joined to. We then use a Viterbi search to find the optimal path through the candidate units that minimizes the following expression:
W allows a weight to be set optimizing join cost over target cost. Given that clusters typically contain units that are very close, the join cost is usually the more important measure and hence is weighted accordingly.