Although it is very important to conduct listening tests when constructing a practical sound field reproduction system based on wave field synthesis, listening tests are very expensive. A localization model of synthesized sound images that predicts the results of listening tests is proposed. This model reduces the costs of constructing a reproduction system because it makes it possible to omit the listening tests. The proposed model uses the precedence effect and predicts the direction of synthesized sound images based on the inter-aural time difference. A comparison of the results predicted by the proposed model and the localized results of listening tests shows that the model accurately predicts the localized results.

Deforestation is a well-known program transformation technique which eliminates intermediate data structures that are passed between functions. One of its weaknesses is the inability to deforest programs using accumulating parameters. We show how certain kinds of intermediate lists produced by accumulating parameters can be deforested. In this paper we introduce an accumulative variant of foldr, called rdlof, and show the composition of functions defined by foldr and rdlof. As a simplified instance of foldr and rdlof, we then examine dmap, an accumulative extension of map, and give the corresponding fusion rules. While the associated composition rules cannot capture all deforestation problems, they can handle accumulator fusion of fold- and map-style functions in a simple manner. The rules for accumulator fusion presented here can also be viewed as a restricted composition scheme for attribute grammars, which in turn may help us to bridge the gap between the attribute and functional worlds.