### ASA 124th Meeting New Orleans 1992 October

## 2pPP7. Auditory space modeling and simulation via orthogonal expansion and
generalized spline model.

**Jiashu Chen
**

**
Barry D. Van Veen
**

**
Kurt E. Hecox
**

**
**
*University of Wisconsin---Madison, H6/573, 600 Highland Ave., Madison, WI
53792-5132
*

*
*
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.]