Auditory space modeling and simulation via orthogonal expansion and generalized spline model

Abstract

A two-stage model that establishes a mathematical representation of auditory space is developed. The first stage of the model consists of a low-dimensional subspace representation for the free-field-to-eardrum transfer functions (FETF’s). The bases of this subspace are complex-valued eigentransfer functions (EF’s) obtained from the Karhunen–Loeve expansion of the measured FETF’s covariance matrix. Each FETF is represented as a weighted sum of the EF’s. The second stage of the model is a functional representation for the weights, termed spatial transformation characteristic functions (STCF’s), applied to the EF’s. The STCF’s are functions of azimuth and elevation. A generalized spline model is fitted to each STCF derived from measurements. The spline model filters out noise and permits interpolation of the STCF between measured directions. The FETF’s for an arbitrary direction is synthesized by weighting the EF’s with the smoothed and interpolated STCF’s. Using FETF’s sampled uniformly over the upper 3/4 sphere for one KEMAR ear, it is shown that 99.9% of the energy in the measured FETF’s is contained in a 16-dimensional subspace. The relative average mean-square error between 2320 measured and simulated FETF’s is found to be less than 0.25%. [Raw data provided by Dept. of Neurophysiology, University of Wisconsin−Madison.]